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THE INTERNATIONAL SCIENTIFIC SERIES. 



FALLACIES. 



A VIEW OF LOGIC FROM THE PRACTICAL SIDE. 



BY 



ALFRED SIDGWICK, 

B. A. OXON., 
BERKELEY FELLOW OP THE OWENS COLLEGE, MANCHESTER. 




NEW YORK: 
D. APPLETON AND COMPANY, 

1, 3, and 5 BOND STREET. 

1884. 



^t 



PKEFACE, 



This book is intended, like the others in the Inter- 
national Scientific Series, mainly for the general reader. 
That is to say, it requires no previous technical train- 
ing, and is written as much as possible from the unpro- 
fessional point of view. 

Although any treatment of Fallacies must be to a 
great extent a treatment of methods of Proof, and must 
therefore demand a certain amount of general logical 
theory, yet by trying to keep chiefly in view the practical 
side of the science of Logic, — subordinating to that all 
other interests or inquiries, — I have been able to neglect 
the discussion of much debatable matter and to avoid 
definite adherence to a school. No doubt, Mill and Bain, 
— and, more remotely, Hume, — are the authors to whom 
the general substance of the present work is mainly 
traceable ; but one may, I hope, utilise many of their 
results without being compelled to accept the whole of 
their Philosophy. As regards later writers, although 



VI PREFACE. 

hints have here and there been taken from various other 
sources, English and German, the aid so obtained has 
been, I think (except where expressly mentioned), frag- 
mentary or indirect. 

It is impossible fully to acknowledge all the viva voce 
help received from friends, but I may at least here 
express my gratitude to the anonymous Founder of the 
Berkeley Fellowships at the Owens College. The election 
to one of these, in 1881, has given me the opportunity of 
finishing this book (then already designed for this Series) : 
and has also provided me with the invaluable advice and 
criticism of Prof. Adamson. 

By the courtesy of the Editor of Mind, & portion of 
chapters iii. and iv. (Part I.) is reprinted from that 
Journal. 

Manchester, May, 1883. 



CONTENTS 



INTRODUCTION. 

SECTION * PAGE 

I. Difficulties of Treatment ... ... ... ... ... ... 1 

II. The Practical Side of Logic 11 

III. Outline of the Work 20 



TAKT I. 
PROOF IN GENERAL. 

CHAPTER I. 

THE MEANING AND AIMS OF TROOF. 
I. Proof and Inference 31 

Importance of the distinction, 31. Ambiguities of ' Inference,' 
' Reasoning,' etc., 32-34. The problem of Proof always 
narrower than that of Inference, 35. 

IT. Proving and Testing 35 

Further ambiguities of ' Proof,' 35-37. Its etymological 
meaning, 36. Successful resistance to attack, 37, 38. 
' Practically ' sufficient Proof, 38. Yalue of hostile criti- 
cism, 39. The discarding of rival theories, 40. 



Vlll CONTENTS. 

CHAPTER II. 

THE SUBJECT-MATTER OF PROOF: IN GENERAL. 
SECTION PAGE 

I. Keal and Unreal Propositions ... 41 

A thesis, what, 41. ' Verbal ' and ' Unreal,' 42. Tautology, 
43, 44. Self-contradiction, 44-47. ' Ultimate beliefs ' and 
Unreality, 46. Meaningless terms, 47, 48. Propositions 
apparently, not actually, unreal, 48-51. 

II. Subject and Predicate 51 

* Things spoken of,' 51, 52. Propositions viewed as stating 
a relation, 53-56. Copula, 54. Starting-point and goal of 
an assertion, 54, 55. 

III. Simple and Complex Propositions 56 

No sharp line to be drawn between them, 56. An argu- 
ment, as a whole, is a complex proposition, 58. 

CHAPTER III. 

THE SUBJECT-MATTER OF PROOF: MAIN KINDS OF THESIS. 

I. Indication 59 

All propositions assert ' indication,' 59. Indication and im- 
plication, 60. Special sense of the nams, 61, 62. 

II. Affirmation and Denial ... 64 

III. Abstract and Concrete Propositions ». 66 

The abstract proposition, 66. The concrete proposition, 

67, 71. Exceptive denial, and the assertion of difference, 

68, 70. Concrete denials, 71. Abstraction and abstract 
names, 72. Categorical and hypothetical propositions, 
73. Respective functions of abstract and concrete pro- 
positions, 74 j their interaction, 75-77. ' Overtones ' in 
a concrete proposition, 77# 



CONTENTS. IX 



SECTION PAGE 

IV. Succession and Co-existence 78 

' Plurality ' of causes, and their liability to counteraction, 
80. Indication seldom absolute, 80-82. 'Chance,' 
1 Tendency,' and ' Law,' 81. Laws incompletely true, 82. 



CIIAPTEK IV. 

THE LAW OF COUNTER-INDICATION 84 

The pons asinorum of Logic, 84. ' Presence,' and • absence,' 
as sign and signified, 85. Statement of the law, 86. 
Table illustrating the same, 87. Examples, 87-89. Value 
of the law, 89-93. The disjunctive proposition, 92. Ap- 
plication of the law to concrete propositions, 95. One 
precaution necessary, 96. 



CHAPTER Y. 

THE PROCESS OF PROOF, IN GENERAL. 

I. The Eelation between Thesis and Eeason 99 

Keason indicates Thesis, 100. Material truth of the Reason, 
101. Formal adequacy of the Reason, 102. 

II. Consistency 103 

Principles and their ' logical outcome,' 103. Extension to 
analogous cases, 104. The Maxims of Consistency, 
105-107. The use of names, 107-109. The generic and 
differential elements in the meaning of a name, 108. 
Analogical and deductive consistency, 110. 

III. Formal Adequacy in General Ill 

The ' Reason given,' and the whole ' rationalisation ' of a 
thesis, 111. All rationalisation may be expressed syllo- 
gistically, 111. Proof the counterpart of Explanation, 
111, 112. The Principle and the Application, 113. Value 
of the Syllogism, 113, 114. 



X CONTENTS. 

PAET II. 

THE POSSIBILITIES OF ERROR. 
SECTION L— BEFORE PROOF. 

CHAPTER I. 

PAGE 
INTRODUCTORY ... H7 

CHAPTER Ilf 

THE KINDS OF UNREAL ASSERTION. 
SECTION 

I. Tautology, or Platitude 120 

Causes and results, 120-122. Tautologies sometimes useful 
as Postulates, 122. Common forms of Tautology, 123. 
Finer shades, 124-127. ' The ' meaning of a word, 124. 
Bain's view of verbality examined, 125, 126. The special 
definition, 127. The right to require explanations is 
practically limited, 128. 

II. SELF-CONTRADICTION 129 

Causes somewhat different from those of Tautology, 129. 
• Bulls ' and epigrams, 129. Interval between inconsistent 
assertions, 130, 131. The more dangerous forms, 131. 
The 8o7-ites difficulty, 133-136. Occasional value of vague 
assertions, 137. 

III. Meaningless Term 138 

Self-contradiction within a term, 138-140. Belief in 
mysteries, 140. Limits to power of defining, 141. Sum- 
mum genus, 141. Indefinable terms, 142. Ignotum per 
ignotius, 142. 

IV. Unreal Assertion : Concluded ... 143 

Recapitulation, 143, 144. Verbal questions, 144-146. De- 
grees of ' reality,' 146. 



CONTENTS. XI 



CHAPTER III. 

PAGE 
THE BURDEN OF PROOF 148 



The objection 'no evidence,' 148. Self-evident truths, 
149, 150. The frustration of disproof, 150. Distinction 
between denial and doubt, 150. The simple rule, 150, 151. 
Its extreme cases, 151-154. The sceptical position, 153. 
The stifling of inquiry, 154. Whately's doctrine examined, 
154-156. How far bound to explain away facts ? 157, 158. 
The doctrine of ' fair presumptions,' 158-161. Treatment 
of conflicting facts and awkward questions, 161, 162. 
Artificial and natural laws of discussion, 163. Provisional 
theories, 164. Presumption of weakness, 165-167. The 
need and the demand for Proof, 165. Causes of absence 
of Proof, 166. 



SECTION II.—NON SEQUITUR. 
CHAPTER IV. 

INTRODUCTORY 168 

Non sequitur co-extensive with failure in formal adequacy of 
the Reason, 168. A compromise required between Method 
and Guesswork in detecting fallacies, 169-173. Four 
meanings of 'Fallacy,' 172, 173. Reduciio ad absurdum, 
174. 



CHAPTER V. 

THE EMPLOYMENT OF GUESSWORK. 
SECTION 

I. General and Special Sources of Fallacy 176 

Aristotle's plan of division, 176. Mill's plan similar, 177. 
The same plan largely adopted in common use, 177. 



Xll CONTENTS. 

SECTION PAGE 

II. A List of General Objections to any Argument ... 178 

Four main general objections, 178. These four convenient 
but overlapping, 178-181. We must limit their meaning 
by special definition, 182. 

III. The Objection Ignoratio Elencui 182 

Three senses of the term, 182. Dangers of bringing this 
accusation, 183-185. Logic and Grammar, 183. Use of 
the Law of Excluded Middle, 185. Snares of language 
inexhaustible, 186 ; and practically inevitable, 187. Ob- 
jections that miss the point, 188. Finer shades of the 
fallacy, 188-191. Change in the meaning of words, 189. 
Meaning relative to a standard, 191. A broad rule for 
practice, 192. 

IV. The Objection Petitio Principii 193 

Similar difficulty in fixing the meaning, 193-195. The 
meaning here taken, 195. Means of escape from the 
accusation, 196, 197. Resemblance to Platitude, 198. 
Question-begging names, 198, 199. 



CHAPTER VI. 

THE EMPLOYMENT OF GUESSWORK: CONTINUED. 

I. The Objection 'A Factor overlooked' 201 

Faults of the name, 201. Forms of this fallacy really few 
and simple, 202. 

II. The Types of Argument ... 202 

§ 1. Introductory. 

§2. Demonstration and Real Proof 203 

Our neglect of this distinction, 203, 212. Real argu- 
ments and Real propositions, 204. Meaning of 
' Demonstration,' 204-207; of Conclusive proof, 205 j 
and of Necessary truth, 207. Immediate and Mediate 
demonstration, 208. Causes of faulty demonstration, 
209. Demonstrative arguments rare, 209, 210. 
Omitted links, 210, 211. 



CONTENTS. XII 1 

PAGE 

§ 3. Induction and Deduction ... 212 

Deductive and inductive proof, 212-214, 219. Theory 
and fact, 213. All proof deductive, 213. Difficulties 
of the distinction, 214-218. Proof of theory by 
congruent fact, 219. And by recognized law, 219. 
§4. Certain Minor Distinctions ... ... ... ... 220 

Conclusive and presumptive proof, 220. Circumstantial 
evidence, testimony, hearsay, 221. Hypothetical 
and categorical arguments, 221-223. Moods of the 
Syllogism, 223. Ad personam, ad verecundiam, ad 
populum, 223. 

§5. The Argument by Example 224 

Difference from proof by circumstantial evidence, 

224, 225. Subdivision to be made, 226. 
(a) The Argument by Analogy ... ... ... ... 226 

Indistinct resemblance, 227. Degrees of resem- 
blance, 227. Points of resemblance, 228. Essen- 
tial points of resemblance, 229, 230. Formula for 
analogical argument, 230. Difficulty of dis- 
tinguishing analogy from deduction, 231, 233. 
'Parallel cases,' 233. Connexion between ana- 
logical and deductive arguments, 234. 

(&) Proof of Law from Fact 234 

A generalisation not always expressed as abstract, 
235. Eeasons for choosing the abstract propo- 
sition as typical, 236. The ' essential element ' 
of the cause, 237, 238. Formula for the induc- 

1 6. The Argument by Sign ... ... ,., ,,, itf 239 

Middle term may always be viewed as a sign, 239: 
but need not always be so viewed, 240. Simplest type 
of deductive argument, 240. Second type, — ' Distinc- 
tion by point of difference,' 241. Third type, — ' Ex- 
ceptive disproof,' 241, 242. Two varieties of the last, 
242. Precaution in accepting these distinctions, 243. 

(a) Proof by Sign 244 

Generality of the sign required, 244, 245. Nota 
Notce, 245. Names as labels, 245. 



XIV CONTENTS. 

PAGE 

(b) Distinction by Point of Difference ... 246 

Indistinct difference, 246. Essential difference 
247, 248. Negative character of this argument, 
248. 

(c) Exceptive Disproof ... ... ... ... ... 249 

The exception proves the rule, 249, 250. Difficulty 
of proving a negative, 250, 251. Value of ex- 
ceptions, 251, 252. 

SECTION 

III. The Dangers of the Argument by Example ... ... 252 

(a) The Dangers of Analogy. 

Neglect of difference, 254-259. Analogy worthless for 
proof, 256. Analogy, metaphor, and naming, 259. 
An example of loose analogy, 259, 260. When 
allowable, 261. Open reliance on analogy rare, 
262-264. Metaphorical and direct use of names, 
264-266. The employment of proverbs, 266. The 
assertion of essential resemblance, 266, 267. The 
vital point of an analogy, 267. 

(b) The Dangers of Induction ... ... ... ... ... 267 

Degrees of strength in ' indication,' 267-270. ' Tenden- 
cies,' 268. Sole cause, etc., 269. One primary 
danger in induction, 270. Undue neglect of differ, 
ence, 270-273. 'Best' explanation, 271, 272. 
Guarding against undiscovered exceptions, 271. Two 
opposite modes of missing the ideal, 273. Use of the 
Theory of Probabilities, 274. Exclusion of alternative 
theories, 275, 276. Need of analysis, 276. 

(c) The Empirical Methods 277 

The use of the methods, 277. Number, and kind, of 
' congruent facts,' 279. Importance of analysis, 279. 
Attack on a generalisation, 279-281. Methods of 
agreement and difference fundamental, 281. The 
distinction between them unimportant for our pur- 
pose, 282. The proof of laws from facts, 283, 284. 
Ubiquity of ' unknown antecedents,' 284. Results of 
this section, 285, 286. 



CONTENTS. XV 

SECTION PAGE 

IV. The Dangers or the Argument by Sign ... ... ... 286 

CoMses of faulty deduction various, 287. Acceptance of 
a Principle which does not apply, 288. Ignorance of 
syllogistic requirements, 288. Earity of purely syllogistic 
fallacies, 289. Acceptance of reciprocal as equivalent, 
290-292. Fallacia accidentis, 292-297. Neglect of differ- 
ence, 295. Neglect of resemblance, 296. 



CHAPTER VII. 

REDUCTIO AD ABSUEDUM .' ... C98 

Where guesswork fails, what then? 298. Meanings of 
Reduction to Absurdity, 299. The further assertion re- 
quired in a 'real' argument, 299-301. Gaps in the 
reasoning, 301. Axiom of the syllogism, 301, 302. 
Dictum de singulo, 301. Uniformity of Nature, 302. The 
case where the application is direct, 303. Extent of the 
Principle involved, 301-307. Interrogative form of 
the method, 307. The case where the Application is 
remote, 308. The method in Analogy and Induction, 
309, 310. Examination of rival theories, 310, 311. The 
negative attitude, 311-313. 



CHAPTER VIII. 

SOME OBJECTIONS TO LOGIC ... 314 

Practical objections broadly divisible into two groups, 314. 
Hindrance to action, 314-320. Fallibility of Science, 316. 
Value of Error, 317-320. Clumsiness of Logic, 320-3? L 
Common-sense, and intuition, 321. Need for deliberate 
reason and an objective standard, 322-324. 

CONCLUSION. 
Summary % t 325 



XVI CONTENTS. 

APPENDIX. 

PAGE 

A. Alternative Possibilities ... 333 

Events, to be named, are abstracted, 333. The various 
ways in which any two events may be related to each 
other in Causation, 334-338. Co-existent events, 335-338. 
Co-existent qualities, 338. Use of the empirical methods, 
339. 

B. The Empirical Methods in Detail ... 339 

Mill's five methods really two, 339. The two Axioms, 340, 
341. Method of Agreement, 342. Joint Method, 344. 
Method of Difference, 345. Method of Eesidues, 347. 
Method of Concomitant Yariations, 348. The Methods, 
in general, 351. The further evidence required, in em- 
ploying each method, 351, 352. Simplex enumeratio, and 
Post hoc, 352. 

C. The Moods of Exceptive Disproof ... 353 

Reductio per impossibile, 353. The fourteen moods reduced 
to two, 354-356. 

D. Invariable Succession ... ... ... 356 

Cause and ' history,' 356. 'Invariable law' and 'identity* 
of cause and effect, 357. Unconditionality (Efficacy), 
358. 

E. Tables. 

I. Abstract and Concrete Propositions. 
II. Succession and Co-existence. 

III. The Questions arising from Proof. 

IV. The Types of Argument. 

Y. The Dangers peculiar to the special types of Argument. 



RECEIVED. v * 




FALLACIES 



INTRODUCTION. 

I. Difficulties of Treatment. 

Logic holds what may well be called an uncomfort- 
able position among the sciences. According to some 
authorities it cannot be properly said that a body of 
accepted logical doctrines exists: according to others, 
the facts and laws that form such doctrine are so com- 
pletely undeniable that to state them is hardly to 
convey new or important information. Hence, if a writer 
on the science tries to avoid truism, and so to give 
practical importance to his statements, there is danger 
both of real but crude innovation, and also of over-simple 
belief in the value of merely verbal alterations. More- 
over, at its best, Logic has many persistent enemies, and 
by no means all of them are in the wrong : so that those 
who view the science as the thief or burglar views the 
law, find themselves apparently supported and kept in 
countenance by others who really have the right to view 



2 FALLACIES. [Introd. 

it as perhaps the artist views the rules that hamper 
genius. Through its deep connexion with Common 
Sense, Logic is often a source of exasperation to Philo- 
sophy proper : while Common Sense on the other hand 
is apt to dread or dislike it as unpractical or over-fond 
of casuistical refinements. Failing thus to win a steady 
footing, it turns, sometimes, to Physical Science for a 
field of operations : but Physical Science has its proper 
share of boldness, and often leaves the cautious reasoner 
behind. As for Art, — which finds even Common Sense 
too rigid, — here Logic is liable to meet with opposition 
at every grade ; from the righteous impatience of poetic 
souls that are genuinely under grace, down to the in- 
coherent anger of mere boastful vagueness, or to the 
outcry of the sentimental idler. 

In the midst of these perplexities, it is difficult to 
choose a quite satisfactory course. Some excuses may, 
however, be offered for the line that has here been 
taken ; and, first, I would plead as against the charge of 
irregularity or presumption the fact that I have wished 
to keep a single purpose in view, avoiding all questions 
that fail to bear directly upon it. Usually, in works on 
Logic, the object has been to say something valuable 
upon all the questions traditionally treated as within the 
field of the science, and, in attempting this, the single 
practical purpose is apt to become obscured. It is only 
in consequence of my avoidance of side-issues that any 
appearance of novelty in the treatment has followed. 
Moreover, it is not teaching, but suggestion that is chiefly 



Introd.] DIFFICULTIES OF TKEATMENT. 3 

here intended. It is always allowable to write rather 
in the co-operative spirit than the didactic, and this 
has certainly been my aim throughout. And the same 
apology may apply to the charge of forcing verbal 
changes upon the reader : the novelties of statement are 
here put forward merely as possible aids in keeping 
our single purpose clear, and, in fact, I found them almost 
unavoidable. 

As regards the points where Logic might seem to 
clash with the furthest or deepest Philosophy attainable, 
the plan adopted has been to avoid all controversy by 
restricting our discussion to the questions that arise 
before such deepest Philosophy begins. Without ad- 
vancing any opinion on the merits of metaphysical 
inquiry in general, or on any of its particular results, I 
wish to confine attention to a totally different set of 
problems. 

As regards Physical Science, it must be confessed 
that Logic merely follows after it, systematising methods 
already adopted there, and found to lead to good results. 
And I hold that to combat Fallacy is the raison d'etre 
of Logic ; and that Science, though not infallible, is more 
free from discoverable fallacies than any other field of 
thought. Again, while experimental methods may no 
doubt be capable of much improvement, it seems a 
tenable view that this duty should be left to a special, 
and very advanced, department of inquiry. There might, 
perhaps, be formulated a system of advice for Discovery 
in general, — rules and hints important even to the 



4 FALLACIES. [Introd. 

leading men of science. But in the meantime, Logic (as 
usually understood) can hardly help containing a good 
deal of elementary matter, and is compelled to take for 
granted in the learner a power of making very elementary 
mistakes. It seems that the best Scientific Discovery 
must always be in advance of Inductive Logic, in much 
the same way as the best employment of language runs 
in advance of Grammar. Still, there may be some use in 
tiying to direct and help those who are not already 
scientific, or only in the earlier stages of the pursuit ; nor 
need the name of Logic compel logicians to claim a 
dignity beyond their power. One cannot fulfil success- 
fully the duties of Lord Chancellor and Justice of the 
Peace at once. 

As regards Common Sense, it is a little more difficult 
to avoid coming into conflict here ; since there are plainly 
two kinds of Common Sense, — one the essence, and the 
other an undying enemy, of the most perfect use of 
reason. Against near-sighted dogmatism, or the self- 
satisfied refusal to see distinctions, or the habit of slurring 
over awkward facts, Logic always intends to carry on a 
war : but we need not therefore assume that depth or 
distance of vision, or the practice of splitting hairs or of 
raising ingenious doubts and difficulties, can never be 
pushed beyond the limit at which they possess a practical 
value. The drawing of this line is a standing difficulty 
which cannot be settled off-hand, but needs the utmost 
patience : at present, it seems to me, one can only admit 
the difficulty and remember that the needs of practice 



Inteod.] DIFFICULTIES OF TREATMENT. 5 

have an older and more final claim than those of 
curiosity. And, mutatis mutandis, the same applies to 
the objections from the side of Art : here, also, two 
different spirits may be clearly distinguished, one fighting 
really on our side, though perhaps by other methods, 
and the other fighting against us indeed, but an enemy 
deserving little else than contempt from healthy people. 

But perhaps the special difficulty in the case of 
Common Sense is that to the simple-minded all things 
are simple and straightforward. The knowledge of 
difficulties and of dangers is already an advance beyond 
mere childish innocence of evil. As Mrs. Farebrother, in 
Middlemarch, is made to say, " When I was young, Mr. 
Lydgate, there was never any question about right and 
wrong. We knew our catechism and that was enough ; 
we learnt our creed and our duty. Every respectable 
Church person had the same opinions. But now " — alas ! 
the reverence for easy-going certainty is lost. So in the 
kindred question of bodily disease : to our grandfathers, 
and still more to their grandfathers, diseases were few in 
number but quite unmistakeable when they came : pre- 
monitory symptoms were almost things unknown, and 
degrees of health were only reluctantly admitted possible. 
And yet the death-rate is decreasing : our ancestors died 
by thousands of diseases which we are conquering. Very 
similar is still to a great extent the attitude of Common 
Sense towards Fallacy. " Did God make men two-legged 
only, and leave it to Aristotle to make them rational ? " 

Nothing is harder than to induce short-sight or super- 

2 



6 FALLACIES. [Introd. 

ficiality to believe that any extension of view or of 
insight exists beyond that to which Common Sense is 
accustomed: although the actual telescope and the 
microscope cannot now be treated as mere toys, yet out- 
side the realm of material objects the telescopic and the 
microscopic spirit is still, by many, considered almost 
worse than useless. The general reader has, in fact, a 
rooted belief that Logic is a highly unpractical body of 
doctrine : unpractical perhaps not only through short- 
comings of its own, but from the supposed fact that no 
one but an absolute fool can ever commit a fallacy. Is 
not the light of Nature worth more than all the reason- 
ings of all the logicians that ever lived ? Such an appeal 
to idleness is always sure to win a large amount of ready 
applause. The view here taken, on the contrary, is that 
many things are believed in the name of Common Sense 
which a higher Common Sense would condemn, and that 
no one who is merely human can avoid fallacy altogether 
for a day. 

Another fact moreover which operates to prevent any 
widespread interest in Logic is, no doubt, its barrenness 
in surprises. In all the physical sciences, Common Sense 
is being constantly forced to acknowledge that its 
methods are not so infallible as our fathers fondly 
supposed. Even the question " Am I not to believe my 
own eyes ? " carries no longer the same conclusiveness as 
formerly, while every day some new portion of firmly 
held popular faith is shown to have been delusive or in- 
complete. Nor is it only in what are commonly called 



Intkod.] DIFFICULTIES OF TREATMENT. 7 

the Physical Sciences that this is the case. Political 
Economy, though it depends so largely on mere careful- 
ness and consistency of thought, is rich in unsuspected 
facts. In Mental Science, and perhaps in Ethics, a 
harvest of surprises is ripening. But in Logic the case is 
different. The central practical doctrines of Logic have 
been so long ago made common property that to a great 
extent they have passed into commonplace: which is 
much the same as saying that they commonly command 
verbal assent too readily for real assent to be strong. 
They lose the strong support that comes from conquered 
doubt, and through supposed familiarity pass into real 
oblivion. Hence it is chiefly in generalising what is 
already known, and so preserving it in a shape more 
easy to remember and apply, that the value of Logic 
consists. And therefore it is difficult to prevent its 
doctrines being tedious or exasperating, even where they 
may be most required. 

There are one or two minor objections to the study 
of Logic, — even practical Logic — which may be just 
mentioned here as possible stumbling-blocks. One some- 
times hears, for instance, that there are so many systems 
of Logic all at variance with each other that the puzzled 
inquirer cannot tell which to accept. On this it seems 
sufficient in the first place to remark that Logic does not 
claim to be a sort of revelation, which any one is requested 
to 'accept' at all, but rather a labour-saving apparatus 
which each may usefully alter somewhat to suit his own 
particular needs. Again, it is hardly too much to say that 



8 FALLACIES. [Introd 

whether the inquirer thinks for himself, or accepts the 
system of any one logician or of all, the result for practical 
purposes will be precisely the same, except perhaps as to 
speed in learning. In all that is essential to practice 
there is not only no difference of opinion but room for 
none. The disputed ground of Logic lies wholly outside 
that science when viewed as a machine for combating 
Fallacy. The disputed points refer, without exception, 
either to the question of the proper province of the 
science, or its convenient arrangement, or to the adja- 
cent subjects of Metaphysics, Psychology, Rhetoric, or 
Grammar. 

Another objection, only to be mentioned as unim- 
portant, is that the study of Fallacies belongs altogether 
to Rhetoric rather than to Logic, and to Rhetoric in a 
degraded form The effect of a study of Fallacy, it seems 
to be sometimes feared, must be to make us tricky, or at 
least to lead to wordiness and mere ingenuity of repartee. 
But let us at any rate meet part of this objection by our- 
selves refusing to let a harmless word offend. If the name 
Rhetoric be preferred let us accept that name without 
hesitation, And as to the question of fact, of the actual 
effect of a study of Fallacies, that of course is a matter 
on which there is ample room for difference of opinion, 
and I firmly believe that such study has on the whole a 
depressing and disarming effect on the power of being 
successfully sophistic, even where the will to deceive is 
present. For really effective sophistry nothing is so 
vitally requisite as semi-innocence. Just so far as the 



Inteod] DIFFICULTIES OF TREATMENT. 9 

epigram holds true that unconscious hypocrites are the 
greatest hypocrites of all, so may we say that the self- 
deceiver is the most successful sophist Of course, by 
definition, Fallacy and Sophism are distinct, — the latter 
is clever deception, the former only honest error ; but the 
line between them is in real life so dim and wavering 
that the distinction is practically useless for most 
purposes except that of giving our neighbour an un- 
complimentary name. Witness the case of the highly 
respectable, and even honourable, man who late in life 
begins to find cherished theories unstable. By the 
hypothesis his defence of them can be considered pure 
fallacy no longer, and yet would it not be cruelly unfair 
to class him with conscious sophists ? Effective sophistry 
of the more conscious kind can only take place either 
where the audience are immensely beneath the sophist 
in acuteness or where they are positively eager to be 
deceived. And these may, from a general point of view, 
be regarded as exceptional cases. We are mostly subject 
to the criticism of our equals, and the real belief is widely 
held that, after all, truth so far as attainable is an end to 
be desired. 

Another objection sometimes heard is that there is 
danger in tampering with mother- wit by substituting for 
it the highly abstract, narrow, inelastic rules of Logic. 
Real life, it is said, is large and complex and many- 
sided. To deal with actual problems successfully, a 
quickness and breadth of perception are needed, which 
must be largely unconscious, under pain of being in- 



10 FALLACIES. [Introd. 

complete. Much in the same way as the hard rules of 
grammar are vexatious to those who know their mother- 
tongue, or as a deliberate effort to remember how to 
spell a word is apt to raise needless doubts and difficul- 
ties, so, it is sometimes held, does highly conscious 
reasoning produce more evil than it conquers. This 
objection has some real force, and in our last chapter 
there will be occasion to speak of it again. At the 
present stage it may be sufficient to remark that although, 
no doubt, a little knowledge is a dangerous thing, yet 
rightly understood that fact is, in ordinary circum- 
stances, merely an argument for trying to attain as 
much knowledge as possible. The fact of the danger 
once recognised too, it becomes to a great extent disarmed. 
The amount of knowledge required to get beyond the 
dangerous stage in Logic is easily attained : and with or 
without that knowledge the application of Logic is mainly 
dependent on practice rather than on theory. All that 
theory can expect to do in the matter is to clear the 
way, and so to economise a great deal of time at the 
beginning. No book on Logic can be used as a vade- 
mecum, — carried in the pocket and consulted when in 
doubt whether to take a cab or not, and in other daily 
difficulties of the kind. If any reader is inclined to 
expect such aid he will certainly be disappointed. The 
point of view and the expectations must be altered, 
or there will be little good to be got from any book. 
Nothing can be a complete guarantee against all fallacy ; 
nor can Logic be made an instrument for testing or 



Intuod.] THE PRACTICAL SIDE OF LOGIC. 11 

judging off-hand the truth of all possible propositions 
put forward. 



II. The Practical Side of Logic 

We are, then, not here properly or directly concerned 
with any of the disputed questions of Logic : we need 
not even discuss the nature of that science or the limits 
of its province. And yet the matters we shall have to 
treat constitute in themselves the main thread which 
runs through all logical doctrine, and the final object for 
which it has been developed. By making the practical 
purpose of Logic the central point of interest, we help to 
gather up and bind together its disconnected parts 

Logic may in fact be viewed a3 a machine for 
combating Fallacy. Like all machines, too, it is itself 
capable of much improvement in the certainty, the pace, 
and the fineness with which it performs its work. But 
unlike machines of lifeless material, its final purpose is 
in constant danger of being forgotten for other interests, 
as men sometimes lose sight of their main intention, take 
means for ends, and become misers or enthusiasts. Logic 
is rather a living organism than purely mechanical, and 
it is full of rudimentary organs which have historical 
and explanatory interest, but not all of which are now 
any longer useful for performing work or preserving the 
life of the science. The Logic required for examinations 
is thickly over-grown with disputed questions properly 
belonging to other departments of inquiry : and though 



12 FALLACIES. [Introz?. 

many of these discussions are of great value in them- 
selves, and some perhaps also for developing still further 
the theory of Logic ; though no one can consider himself 
a thorough student of the science until he knows, at least 
in broad outline, the history of these disputed questions, 
yet there are points of view from which we may use- 
fully neglect them, may avoid all doubtful matters, fix 
attention solely on the practical means of fighting fallacy, 
and, as preliminary, sum up the admitted doctrines 
which bear directly on that purpose, to the exclusion of 
all the rest. We shall neglect, therefore, all inquiry into 
the proper ' province ' of Logic. If any reader prefers 
any other name for the doctrines here treated, no objec- 
tion will be raised. It is our business to inquire what 
the doctrines bearing on the above-mentioned purpose 
are, not what they may best be called. If through the 
employment of a wrong name any discoverable error 
should arise at any point, that point will present a con- 
venient opportunity for correcting our definition. Pro- 
visionally, however, and with this apology, we may use 
the name of Logic. 

Next, we shall neglect, as said above, all ' ultimate ' 
questions ; all questions of purely metaphysical interest. 
And here it seems necessary to remove a possible miscon- 
ception. There is an active hostility to Metaphysics 
which has exasperated some metaphysicians into declaring 
that we cannot do without them. Metaphysics of some 
sort, they tell us, there must be. The only alternative 
is between good metaphysics and the cheap substitute 



Introd.] THE PRACTICAL SIDE OF LOGIC. 13 

that Positivism provides. Without stopping to inquire 
whether possibly other alternatives might be discovered, 
I may remark that what is here meant by neglecting 
metaphysical discussions is simply leaving the decision 
of the question which system of metaphysics is, on the 
whole, the best, until some occasion when the pressure 
of more immediate practical needs has been relieved. 
The most ardent metaphysician would hardly contend 
that an unexceptionable system of metaphysics is a 
necessary of daily life ; and it is entirely with explana- 
tion and prediction regarded from an everyday point of 
view that we are here concerned. Having satisfied more 
immediate needs, readers can proceed for themselves 
afterwards to the more remote. The attempt to begin 
with Metaphysics, however natural it may be, is rather 
too much like attempting to write a flowing hand while 
we ought to be practising pothooks. It is a fair descrip- 
tion of the ' practical ' spirit in Logic, to say that it 
consists chiefly in the intentional neglect of these deepest 
difficulties. 

We start at any rate with all assumptions on which 
the meaning and use of language depends; and with 
those which are necessary in order that explanation and 
prediction (for practical purposes) should be possible. 
We assume, for instance, that the distinction between 
the subjective and objective Universe has a real value ; 
and also that the whole Universe may be usefully 
parcelled off into definite 'nameable things,' — objects, 
qualities, events, and classes of these, — which, for all 



14 FALLACIES. [Introd 

practical purposes, may be viewed as consistently break- 
ing its continuity. As corollaries to the second of 
these assumptions, or as an amplification of it, we may 
accept the formulae known as the 'Axioms of Con- 
sistency,'* — the Laws of Identity, Contradiction, and 
Excluded Middle. Secondly, as regards the Metaphysics 
of Causation, we avoid the ultimate difficulties simply 
by stopping short before they are reached, and by con- 
fining our attention to what may be called a lower point 
of view. We assume the existence of uniformities in 
Nature, — natural laws ; the narrowing down of these 
into exactitude being the endless problem of discovery, 
and the completest knowledge of them already attained 
at any period being, for that period, the basis of all 
explanation, prediction, and proof. 

The difficulty of keeping the discussion of Fallacy 
clear of psychological questions will be obvious to all 
readers of Mr. Sully's recent work on Illusions ; but the 
scientific treatment there given, a treatment of the 
subject directly from the psychological point of view, 
helps to absolve us here from attempting to deal with 
its difficulties. Logic is always in some danger of en- 
tanglement with Psychology, but by keeping the practical 
purpose prominently in view, we probably avoid, better 
than in any other way, confusion between the two 
distinct sets of questions. It is only with the regulative 
laws of thought that Logic has any direct concern. What- 
ever psychological doctrines may be here occasionally 

* More properly ' Postulates.' Also called ' Maxims : ' cf . infra, p. 105. 



Introd.] THE PRACTICAL SIDE OF LOGIC. 15 

appealed to, must accordingly be considered as of quite 
secondary importance. 

Ao-ainst confusion with Rhetoric we shall find it more 
difficult to guard. The connexion between Practical 
Logic and Rhetoric is extremely close, and for those 
whose interest lies in accurately mapping out the 
boundaries of either science, must no doubt be very 
puzzling. Pthetoric is commonly considered as the 
science of Persuasion (and possibly also of Pleasing) by 
means of language, — persuasion whether to true or to 
false conclusions; and since Persuasion partly depends 
on showing the person to be persuaded an appearance, 
whether real or counterfeit, of truth — of absence of 
fallacy, — the importance to it of a thorough familiarity 
with Logic is obvious. Rhetoric can hardly exist, in 
its most powerful shape at least, without a considerable 
knowledge of the difference between sound and unsound 
reasoning. It may, in fact, on its argumentative side, 
be viewed as an embodiment of Practical Logic, used by 
one person upon another or others, and applied in- 
differently either in aid of the purposes for which Logic 
properly exists, or in antagonism to them. But though 
Rhetoric cannot exist without Logic, the latter science 
can, it seems to me, exist apart from the former. As Hill 
expressed it, if there were but one rational being in the 
universe, that being might be a perfect logician ; Logic, 
in this sense, is in fact simpler than Rhetoric, and 
preliminary to it. 

The connexion between Logic and Grammar is per- 



16 FALLACIES. [Introd. 

haps not quite so confusing, though still not altogether 
easy to avoid. Both Logic and Grammar sit in judgment 
on the meaning of assertions made. Both are con- 
cerned with the use of language, and both lay down 
rules for its correct employment. In one sense, there- 
fore, Logic may be regarded as only a wider Grammar ; 
not indeed as presuming to dictate the absolute meaning 
of any given set of words, but as legislating unmistakably 
in certain cases on the combined meaning of any two or 
more separable assertions when their separate meaning 
is already agreed upon or declared. While Grammar, 
for instance, tells us that two negatives make an affirma- 
tive, Logic takes a wider view and says in effect " Use 
whatever words and phrases you please (however ungram- 
matical) so long only as their meaning is clearly agreed 
upon j but having agreed on the meaning of vour terms 
and your propositions, two contradictories fill a Universe, 
and to deny the one is to assert the other." The main 
difference, perhaps, is that while Grammar is solely con- 
cerned with enforcing the prevailing fashion in language, 
and thus with preventing solecism, Logic cares not at all 
what the fashion may be, insisting solely that meaning 
shall be in the first place agreed upon, and then con- 
sistently preserved. In Logic, a largeness of interpre- 
tation is needed, which is quite unknown to Grammar ; 
for its sole concern is, through preventing inconsistency, 
to strike at the root of Fallacy. At the same time it is 
not always quite easy in practice to keep the two 
purposes wholly distinct, since Logic finds great con- 



Intboi).] THE PRACTICAL SIDE OF LOGIC. 17 

venience and great economy of time, in making some use 
of accepted Grammar. A certain amount of Grammar, 
as also a certain amount of Psychology, is one of the 
necessary foundations for any effective study of Logic. 
Accordingly, while we shall have occasion sometimes to 
neglect side- questions interesting in themselves, but 
whose interest is of grammatical rather than logical 
importance, yet from our point of view language is a 
necessary instrument, and the accepted rules of its em- 
ployment are of high convenience ; and hence it may no 
doubt be found sometimes a little difficult to separate 
the two interests of Logic and Grammar. 

In short, so far as any question, whether commonly 
treated as a logical one or not, has a direct and obvious 
bearing on the methods of combating Fallacy, to that 
extent it will deserve our consideration: so far as its 
bearing on our main purpose either cannot be traced, 
or is too remote and lengthy for satisfactory treatment, 
to that extent we shall simplify our work by avoiding it. 

The practical purpose of Logic being, then, the 
guidance of our reasoning as safely as possible through 
the dangers to which it is exposed, it remains to explain 
and to limit this purpose more particularly. ' Guidance ' 
is slightly ambiguous, since a set of hints and rules aimed 
purely at increasing our powers of discovery, might fairly 
be held by some to come under this designation. But 
it is entirely with proof that we shall be concerned : 
with the reflection on our inferences, not with inference 
or discovery itself directly. Indirectly, of course, the 



18 FALLACIES. [Introd. 

methods of proof are auxiliary to discovery, but it is of 
great importance to keep the two purposes distinct. For 
proof there must always be in the first place a proposition 
to be proved, or thesis; while, in inference, this is the 
final goal of which we are in search, and which is then 
rightly called the conclusion. Roughly speaking, every 
thesis is of course itself an inference, but an inference 
(or conclusion) does not becomes a thesis for proof until 
we reflect upon our reasoning, and desire to examine the 
strength of our grounds for the belief. Guidance, there- 
fore, must here be taken to mean not the first vague 
hints that may set us on the track of a fruitful inference, 
but the methods for conducting an impartial trial upon 
conclusions already somehow reached. The methods 
of Logic cannot be employed for the direct purpose 
of enabling us to reason, but only for that of enabling 
us to know whether in a given case we have reasoned 
correctly, or at least to discern where the weak point 
in our certainty must lie. 

'Reasoning' too demands explanation. By some 
(e.g. Whately and Hamilton) an attempt has been made 
to restrict the name to the process of unfolding our 
conceptions, syllogising, or concluding from generals to 
particulars ; errors in reasoning being taken to mean 
simply failures in consistency. In this sense of the 
term, a child who had once been scalded through putting 
his hand into a basin of hot water, might be said to 
reason correctly in dreading a basin of cold water on 
the next occasion ; but he would then " reason correctly " 



Introd.] THE PEACTICAL SIDE OF LOGIC. 19 

by means of a premiss materially false, — that premiss 
being of course some such universal as 'All water in 
a basin will scald/ or some such application as ' This 
is hot water/ In another of its senses, to reason is, 
as Mill puts it, simply to infer (whether provisionally 
or reflectively) any assertion from assertions already 
admitted. And since Mill's definition is perhaps most in 
accordance with ordinary usage, and further since it 
enables us to bring under consideration the dangers 
in Inductive or Empirical Proof, it is in this sense that 
we shall here understand the term, adding however that 
it is against errors in reflective reasoning only that Logic 
can at all undertake to guard. 

Methods of guidance might be discussed either from 
the positive side or the negative, — as supplying marks 
by which to recognise either valid evidence or invalid. 
The latter plan, as the name chosen for the book will 
have already shown, is adopted here. Not only is 
Fallacy in many ways more interesting than correct 
reasoning, but this view of the subject seems to me 
to keep before us, more distinctly than could otherwise 
be done, the negative character of practical Logic. The 
application of Logic is on the whole rather restrictive 
than forward-moving. As already said, it does not 
discover, but it proves, or tests, discoveries which claim 
to be already made. Moreover, in proportion as this 
negative or questioning spirit becomes habitual, our 
chance grows stronger of avoiding the character of an 
advocate, and attaining the judicial frame of mind. The 



20 FALLACIES. [Introd. 

first condition of all for avoiding fallacy, must surely 
be, as Mr. Spencer expresses it, " the calmness that is 
ready to recognise or to infer one truth as readily 
as another." But besides this possible disciplinary ad- 
vantage, and on the whole more important than it, the 
fact should be remembered that it is as the enemy of 
Fallacy that Logic must always find its application 
to real life : Fallacy occupies much the same position 
in regard to the science of Proof that disease occupies 
in regard to the science of Medicine. 

In speaking of the negative character of Logic as 
a practical science, we must not however imagine that 
its action on belief is purely repressive. Rather, by 
repressing the natural tendency to undue belief, we earn 
the right to be doubly secure in those beliefs that stand 
the trial well. Of all unpractical habits of mind, the 
purely sceptical habit, so far as it can exist, is perhaps 
the least satisfactory ; and if Logic really led no further 
than this, there would be strong practical reasons for 
determining to blind ourselves to its truths. But perhaps 
it may be found possible to keep the dangers of Proof 
in view, while still remembering the central purpose for 
which this is done; namely, not in order to discard as 
much pretended evidence as possible, but to win security 
in our beliefs, through taking care. 

III. Outline of the Work. 

The war against Fallacy is, I am afraid, far too 
large an enterprise to be undertaken by any one book, 



Ixtbod.] OUTLINE OF THE WOEK. 21 

or indeed by any one author. Whether or no it was 
possible long ago, to survey the whole field of knowledge, 
both in general and in detail, laying down the law for 
all men, and marking out the line between truth and 
falsehood in all departments, nothing of the kind is 
possible now : no one at the present time, — unless abso- 
lutely unaware of the modern developments of Science, 
and its innumerable fields of special research, — will 
presume to offer to his readers, a set of infallible methods 
for keeping free from error. There would be great 
danger, it is felt, of providing something not much more 
practical than Dr. Watts' rules 'for the right use of 
Reason/ 

But there are certain broad laws (which may with 
sufficient accuracy be called Laws of Evidence in general) 
which are perfectly universal in their stringency, and 
which it concerns every one to have at his fingers' ends. 
Properly speaking these are laws, not of evidence itself, 
but preliminary to the operation to which the name 
'judgment of evidence ' is most commonly applied, — laws 
of interpretation (in a wide sense of that term), or, more 
exactly, laws of the implication of one assertion by 
another or others, whether the process of the given 
materia] inference be from the general to the particular, 
or vice versa. The law here called that of ' Counter- 
indication ' * may be mentioned as a typical example of 
what is meant; or the Maxims of Consistency, above 
referred to ; or again, the law that all Proof, to be really 

* Cf. infra, p. 84. 



22 FALLACIES, [Intkod. 

Proof, requires a reference to some wider generality* 
than the thesis. The knowledge of such laws is not by 
itself a sufficient safeguard against all possibility of error, 
but only a prior condition of attaining any safety in 
judging, even with the best possible special knowledge, 
or after the longest ' experience/ Such laws, though in 
reality extremely few and simple, — some even almost 
ludicrously self-evident, — present sufficient difficulties, in 
their application, to render the study of them, in regard 
to such application, a subject well worth careful attention : 
and a part of this task is what lies before us here. 

It is evident that several different purposes in study- 
ing Fallacies may be distinguished. There is, for 
instance, the purely scientific or theoretical interest, 
whether as regards the Psychology of error, or merely 
with the view of obtaining an exhaustive list, and 
a clear tabular arrangement, of its varieties. Or on the 
other hand there is the practical interest (which may 
of course also be in the best sense scientific), leading 
to a survey of the methods of combating Fallacy in the 
shapes in which it actually occurs. And under this 
second head certain quite distinct purposes must further 
be noticed as possible. The methods of combating Fal- 
lacy admit broadly of three quite separable developments : 
there may be methods for (1) simply detecting fallacies 
already committed by ourselves or others ; or (2) for con- 
victing others of such errors when found ; or (3) methods 
aiming at the attainment of the completest infallibility 
* Cf. infra, pp. 112, 213, 329. 



Introd.] OUTLINE OF THE WORK. 23 

possible. Or, as we might more briefly express the same 
division, methods of diagnosis, cure and prevention. 

Of these various subjects, our purpose here will be to 
neglect (as said above) the Psychology of error, and to 
aim at obtaining only such classification of the various 
possible forms of Fallacy as shall be of use for one 01 
more of the three practical purposes above mentioned. 

Next it may be remarked that, of these three, the 
last would be a truly desirable accomplishment, but that 
the total avoidance of Fallacy being a comprehensive 
subject, it seems better to attack it piecemeal, and by 
degrees. The second demands a combination of logical 
and rhetorical considerations for which neither Logic nor 
Rhetoric can be said to be as yet at all prepared : this 
subject, if less comprehensive than the last, presents at 
any rate a dangerously complex problem. Even the first 
question (the detection of Fallacy), if it is to be treated 
in any thorough manner, offers practical difficulties which 
might well render us content with a less ambitious aim : 
but since this first question is really preliminary either 
to success in controversy, or to the avoiding of Fallacy, 
the most effectual course appears to be to inquire in the 
first instance what can be done towards the accomplish- 
ment of this simpler purpose. The power of detection is 
in fact the first stage towards avoidance ; which follows 
gradually, as detection becomes habitual. 

We shall find, however, that this purpose itself admits 
of being divided further. Some only of its elements, as 
preliminary to the whole problem of the detection of 



24 FALLACIES. [Intbod. 

Fallacy, will constitute the matters for our consideration. 
As already said, we shall be concerned mainly with the 
methods of Proof and Disproof, and with the points at 
which any case of attempted Proof or Disproof is liable 
to break down. In this way, at least, a rough ground- 
work will be laid, from which any of the practical 
questions may afterwards be approached. The mere 
laying of such foundations should of itself help materially 
in the detection and avoidance of Fallacy, — though it can 
of course contribute nothing to their exposure so far as 
this lies beyond and outside detection. 

Shortly, then, the work before us is to survey, 
classify, explain, and illustrate the possible objections 
which can be brought against any belief, so soon as it is 
definite enough to take shape in language, and thereby 
to become a thesis for proof. An exhaustive review 01 
possible objections once taken, the formation of methods 
for detecting and avoiding Fallacies becomes less difficult ; 
and, accordingly, some suggestions are incidentally made 
for carrying on the work towards this goal. 

Since any pretended assertion may be : — 

1. Meaningless : 

2. Mere unsupported assertion : 

3. Insecurely supported : 

this will constitute our main primary division. In the 
first case, of course, cadit qucestio as to the truth of the 
assertion. In the second case we have to reckon with 
the Burden of Proof. And finally, if a reason be given 
for belief, our judgment of its force must depend pri- 



Lntrod] OUTLINE OF THE WORK. 25 

marily on the extent and soundness of our knowledge of 
the methods of proof; afterwards, en our knowledge of 
the special subject in question. 

" People talk about evidence," it has been said, " as 
if it could really be weighed in scales by a blind justice. 
No man can judge what is good evidence on any par- 
ticular subject, unless he knows that subject well." This 
is perfectly true : knowledge of the special subject is 
required before we can judge of the material truth of all 
that our reasons formally imply. But so long as igno- 
rance of these formal implications themselves exists, the 
methods of Logic have useful work to do. It is just in 
making clear what these formal implications are, — in 
making us aware of the full extent of our assertion when 
we bring forward any reason in support of any thesis, — 
that the central practical interest of Logic consists. 
Beyond this, in fact, it cannot go : in Logic as in Law 
Ignorantia facti excusat, ignorant ia juris non excusat 
It may be added, however, that there is no immediate 
danger of Logic's occupation coming to an end. People 
still commit purely logical blunders, quite apart from 
any ignorance of the special subject. 

Next, whatever reason is given in support of an 
assertion made may fail to prove it in either of two 
ways. It may be : — 

(1) Materially false, even if sufficient : 

(2) Formally insufficient, even if true : 

With the truth of the Reason given we have nothing to 
do in Logic. That is to say, we can only call for its 



26 FALLACIES. [Introd. 

supports, for the supports of these again, and so on until 
we reach some ground sufficiently firm. Accordingly, 
a knowledge of the requirements of formal adequacy 
(apart from the question of material truth) is not only 
all that any science of Reasoning can provide, but so far 
as complete, would be a safeguard against all discoverable 
error. The point at which logical doctrine per se falls 
short of this complete success, has been above vaguely in- 
dicated. Later we shall be in a better position for seeing 
more definitely how far the help of Logic alone can carry us. 

Finally, the reason or reasons given in support of an 
assertion either include in themselves the meaning of 
that assertion or do not. In the former case the question 
as to their material truth becomes at once all-important ; 
in the latter case the central operation of Logic begins. 
For if the Reason given does not already include the 
Thesis in its meaning, some other assertion is required to 
complete its binding force : and it is in the adding of 
this further assertion that all the danger lurks. The 
theory of Proof in general will guarantee our supplying 
the further assertion correctly ; while it is the question 
of the material truth of such further assertion that often 
depends in great measure on our knowledge of the special 
subject. 

Our work, therefore, will consist first of all in a pre- 
liminary survey of the nature of Proof in general, its 
subject-matter and its process. Having cleared the 
ground in this manner, we shall proceed to take in detail 
the objections which can possibly be brought against 



Iktbod.] OUTLINE OF THE WORK. 27 

any assertion, dealing first with those objections which 
arise before Proof begins, and afterwards with the various 
points at which any case of attempted Proof is liable to 
frustration. Under this last head will be found, in one 
sense, the main difficulty; since here we shall have to 
consider to some extent the different dangers introduced 
by the different varieties of Proof. It is hoped, however, 
that these minor distinctions will not unduly obscure 
our more general view. In all cases where real (as op- 
posed to verbal — Cf. p. 204) reasons are brought forward 
in support of an assertion, the operation of Logic consists 
in forcing into explicitness whatever is implied beyond 
that which directly appears. The central point of in- 
terest throughout is the accurate determination of the 
further assertion implied in giving any Reason in support 
of any Thesis. 



PART I. 

PROOF IN GENEBAL. 



CHAPTER I. 

THE MEANING AND AIMS OF PROOF. 

I. Proof and Inference. 

One of the distinctions which it is most difficult, and at 
the same time most important, to keep in view, is that 
between Proof and Inference. In any treatment of 
Logic, confusion of these two separate processes is likely 
to lead to much obscurity; and for us such confusion 
would be certainly fatal, since our main object is to sim- 
plify as far as possible the highly complex problem which 
the avoidance of Fallacy presents, attacking in the first 
place the most preliminary difficulties : and, as will pre- 
sently become evident, the detection of Fallacy is closely 
bound up with the whole question of the needs and 
dangers of Proof, while the attainment of methods for 
rendering our inferences secure corresponds more nearly 
to the wider and deeper problem of avoiding Fallacy 
altogether. 

Nor will it be sufficient for us to rest content with 
the brief and easy-going dismissal of the difficulty which 
is sometimes accepted. It may be perfectly true, as 



32 FALLACIES. [Part I. 

Whately {e.g.) says, that "Reasoning comprehends In- 
ferring and Proving, which are not two different things, 
but the same thing regarded in two different points of 
view : like the road from London to York, and the road 
from York to London ;" but if London happens to be the 
place we want to reach, it becomes a matter of some im- 
portance to distinguish carefully between the two dif- 
ferent directions. It will not suit us to find ourselves 
eventually either in York, or wandering for ever between 
Grantham and Peterborough. For neither of these results 
shall we derive much consolation from reflecting that it 
is " the same road, only regarded from two different points 
of view." 

'Inference' is, in fact, a highly ambiguous word, 
capable of being applied to Proof as well as to Discovery ; 
and all round the question lie a number of further verbal 
ambiguities. When we infer one fact from another or 
others, we believe that fact ' by reason of ' our belief in 
those others ; and when we prove one fact by means of 
another, exactly the same expression is commonly used. 
In both cases there is ' reasoning,' and accordingly both 
that from which the inference is drawn and that on 
which the proof is based are indiscriminately called, in 
popular language, the ' reason.' We reason when we 
proceed from premisses to conclusion, arriving at new 
truths by means of old ones ; and we reason when, having 
already a thesis (an assertion) before us, we produce 
arguments to support it, even if such arguments be then 
for the first time thought of. Again, ' premisses ' is some- 



Chap. I.] THE MEANING AND AIMS OF PEOOF. 33 

times used for the grounds of Proof, and sometimes for 
the data of Inference: 'conclusion' sometimes means 
that which is discovered ; and sometimes that which 
is proved. These ambiguities are probably one great 
source of confusion in the matter ; but besides the merely- 
verbal connexion between Proof and Inference, and per- 
haps in fact a cause of it, there is also a deeper and real 
connexion to which still more of the difficulty may be 
traced. Before we can infer safely, we must prove ; but 
before we can prove, there must be some belief set up for 
proof, and belief (at least in its more definite forms) 
always draws a large part of its life from prior beliefs, 
and is therefore already an inference. There are, in fact, 
'inferences' and 'inferences,' — our first vague guesses, 
and the last assured results of careful inquiry and copious 
hostile criticism. Again, in some cases and to some 
extent, the reasons to which we appeal as proof of a 
given belief are exactly those which in fact led us to 
the belief in question. This is indeed far from being 
always the case, since in very many instances the causes 
of a belief are too numerous or too shadowy to be remem- 
bered in detail, or even to be summed up in any concise 
expression. We need not base this assertion on any 
reference to the more physiological causes of belief : quite 
apart from the uncertainty of these, and even assuming 
the causes of belief to be purely intellectual, who can 
tell exactly why he believes his neighbour worthy or 
unworthy of confidence ? Or who can sum up satisfac- 
torily the multitude of indefinite observations that go to 



34 FALLACIES. [Part I. 

support the judgment, ' That is a well-dressed woman/ or 
'This is a windy sky:' what are the signs, exactly, by 
which we recognise a friend's step, or feel the pulse of an 
audience, or judge some work of art ? In these and many 
other cases only a small part of the real cause can ever 
be given as a reason. Nevertheless, the causes of our 
belief may often be appealed to, if we can remember 
them, as a reason for believing : the same facts may 
be grounds of Inference and of Proof. 

As a preliminary step, then, we may find some advan- 
tage in correcting these ambiguities by the employment 
of two different names. Although 'Inference' might 
no doubt fairly be taken as having both a forward 
and a backward reference, thus covering both fields — 
Discovery and Proof, — there will be great convenience 
in restricting it as far as possible to the former of 
these two meanings ; * and also in keeping the expres- 
sions ' a conclusion ' ' drawn from ' (or 'following from') its 
' premisses ' (or 'data) for the case of Inference, and using 
for the case of Proof the expressions ' a thesis ' ' guaranteed 
by ' its ' reasons ' (or ' resting upon ' its ' grounds '). By 
the name Inference we denote the process of reaching 
a belief: by Proof we mean the process of establishing 
it on a firm foundation after it is already somehow 
reached. The inferred belief, before reflection on its 
validity begins, is not yet a thesis with reasons given : 

* Chiefly because 'Discovery' — the only other name which seems 
at all applicable —is apt to fix attention rather on the result than on the 
process. 



Chap. I.] THE MEANING AND AIMS OF PROOF. 35 

these only come into existence when we begin to test 
the foundations of a belief put forward as secure. 

The problem of Proof is thus always narrower and 
more definite than that of Inference. Instead of asking 
at large ' What conclusion may be drawn ? ' Proof asks 
* Is such and such a given conclusion warranted ? ' In- 
stead of ' What is the cause, or effect, or nature, of A ? ' 
or ' What is the law involved ? ' Proof asks ' Does X 
stand to A in this relation ? ' ' Is such and such a law 
the true one ? ' Instead of having, for answer, to choose 
amongst all the letters of an indefinitely long alphabet, 
Proof has only to decide between the two alternatives, — 
Yes, or No. 

II. Proving and Testing. 

It must not, however, be supposed that by thus con- 
trasting Proof with Inference all has been done that is 
necessary to bring out its full meaning and to avoid 
all ambiguity. Is Proof the finding of guarantees, or 
their examination when already found ? Is it the 
attempt to establish a given belief, or the attempt to 
break it down, or neither of these exactly ? 

In this matter also popular usage is not consistent, 
though on the whole it leans rather to the meaning that 
makes Proof consist in the finding of guarantees. If the 
view here taken be correct, there is a possible reconcilia- 
tion between these apparently opposite meanings, and 
either by itself is merely incomplete. For some purposes, 
no doubt, it may be sufficient to say that proving a belief 



36 FALLACIES. [Part I. 

consists in establishing its truth, but this definition after 
all carries us only a very short way. Nor will it suffice, 
when asked further how a truth is to be established, to 
answer that the process consists in 'stating a valid 
reason' for the belief in question. This, too, is true as 
far as it goes : to prove an alibi, for instance, or to prove 
the defendant's guilt, means to establish the truth of the 
assertion that the defendant was elsewhere, or is guilty ; 
and no doubt the process always consists in showing a 
valid reason why the assertion should deserve belief. So 
again, to prove that the angles at the base of an isosceles 
triangle are equal to one another, means to establish the 
truth of that proposition ; and the manner of performing 
the process certainly is by showing a valid reason, or a 
set of valid reasons, why we should believe it to be true. 
But there is an important fact about the meaning of 
Proof which this explanation tends to make us overlook. 
The word Proof, like so many other words, has under- 
gone a change of meaning in the course of its history. 
In old times, to prove anything meant simply to test it, 
to see what strain it would bear or what fault could be 
found with it. Nothing was implied, one way or the 
other, as to the result of the inquiry : the thing to be 
proved might pass the examination with honours, or 
might fail ignominiously, but in either case the proof 
took place. Thus, " the exception proves the rule " meant 
simply that the exception tries, or strains, the rule : " I 
have bought five yoke of oxen and must needs go and 
prove them " referred merely to the need of trying the 



Chap. I.] THE MEANING AND ATMS OF PROOF. 37 

oxen, or testing their working power. And to some 
extent this old meaning may, perhaps, be said still to 
remain in use; to take a thing 'on probation' still 
allows us to contemplate the possibility of discarding it 
later as useless, to 'probe' is a confessedly tentative 
pursuit, and a lover may ' prove untrue.' 

It is, of course, often misleading to attempt to find 
the modern meaning of a word by tracing its history. 
In very many cases any attempt to bind words down to 
their ancient meaning would lead to serious error. And 
yet if the historical inquiry be properly guarded, it may 
sometimes serve to throw a light on the modern meaning 
which would otherwise be lost or overlooked. We must 
certainly avoid supposing that to prove an assertion 
means nowadays simply to subject it to tests, but at the 
same time by remembering this ancient sense we learn 
some facts about the meaning and aims of Proof which 
are really inseparable from it, and which the modern 
employment of the word rather too much tends to hide. 
Be this, however, as it may, for our purposes at any rate 
it is in attack rather than in establishment that the 
interest lies ; or at least only in such establishment as may 
be won in open battle. Our concern with Proof differs 
from that of the advocate in that we are not interested 
in the finding of evidence to support a thesis, but only 
with the judging of evidence already put forward; or, 
on the other hand, dismissal of the case when all evidence 
is wanting or when no definite issue can be joined. 

Viewing Proof as essentially consisting in successful 



38 FALLACIES. [Part L 

resistance to attack, we in the first place keep before our 
minds the limit of dogmatism beyond which no real 
proof can carry us. It is true that assertions which have 
been tested so far as our tests can go, stand in a better 
position as regards trustworthiness than assertions which 
have not been tested ; and since in multitudes of cases 
the tests applied are amply sufficient for all practical 
purposes, Proof has come in course of time to mean 
chiefly establishment on a sound basis. Even the com- 
pletest establishment of a truth is, no doubt, limited by 
our very finite power of applying tests to it ; but this we 
easily, and for the most part wisely, forget in the pre- 
sence of the plain and fruitful fact that our power of 
testing belief is in so many cases practically sufficient. 
It would be pedantic and absurd to be always re- 
membering that our tests may after all be incomplete. 
When we, or those whom we accept as sufficient 
authority, have tested the assertion that the earth is 
round, or that matter gravitates, it will be found on the 
whole more useful to act on all occasions precisely as if 
those assertions were absolutely true. Having arrived 
at Melbourne by way of Suez, we should hardly, through 
modesty as to the limits of human knowledge, hesitate 
to sail for Europe again in an easterly direction. The 
belief that the earth is round is certainly only proved — 
only tested and not yet found wanting, — but we get from 
our tests, in that case and in many others, a kind 
of certainty which on the whole it is wiser not to 
doubt. Fallible though we are, and incomplete though 



Chap. I.] THE MEANING AND AIMS OF PROOF. 39 

our methods of proof or testing may be, yet there are 
strong practical reasons for considering our knowledge 
in some cases perfectly secure, certain kinds of proof 
sufficiently complete. 

Although, then, simply testing is in this way the 
root-idea, or original intention, of the word Proof, the full 
meaning we shall understand by it is establishment by 
means of tests ; or, more fully, establishment in the face 
of hostile criticism. Not until both sides of a case are 
heard can the verdict claim to be of real value; and if 
we accept a conclusion without considering how far the 
facts will support an opposite one, we do so at our peril. 
Thus, in fixing the meaning* of a name, the point of 
practical importance is where to draw the line, or how to 
distinguish the thing in question from other things ; in 
establishing an explanation, a law of nature, or a pre- 
diction not yet verifiable by the event, the important 
point is to exclude all alternative theories. We know-, 
for instance, what ' work ' is, roughly, and we use words 
like ' civilisation ' or ' honourable ' — and even terms 
aiming at greater definiteness, as ' animal/ ' vegetable,' 
'man/ and 'beast' — with the utmost glibness, and with 
a fair amount of sense : but the whole difficulty of fixing 
their definitions, or settling their exact meaning, begins 
when we attempt to draw the line dividing them from 
their opposites ; when, in fact, we try to justify our 
exclusion of certain candidates for the title. We must 
know clearly what is not work, if we are to find the 

* See also pp. 93, 106, 133, inf. 



40 FALLACIES. [Part I. 

stricter applications of the word; we must determine (if 
possible) where civilisation ends and its opposite begins, 
or what are the exact points of difference which separate 
animal from vegetable, man from beast. Again, before we 
can consider any theory proved, whether such theory be a 
sweeping law, like that of gravitation, or an explanation 
or prediction of some one actual event, we must have 
sound reasons for excluding every possible rival theory. 

This, at least, would constitute complete Proof, if such 
could ever be attained : so far as it falls short of this, our 
proof is weak. The exhaustive examination of alterna- 
tive theories is of course an ideal which we cannot com- 
pletely reach; but the nearer we approach to it, the 
more thorough is our proof, the less assailable our cer- 
tainty. Thus assertions stand on a varying scale of 
credibility: which is only another way of saying that 
evidence varies in strength. 

In proportion as the attacks resisted represent all 
possible attacks, Proof is complete. Hence the importance 
of our central question, — On what grounds can any asser- 
tion be attacked ? And first we need a general view of 
the nature and varieties of assertion ; a classification of 
the questions that may arise for Proof. 



CHAPTER II 

THE SUBJECT-MATTER OF PEOOF : IN GEXEEAL. 

I. Real and Unreal Propositions. 

Having sketched thus in outline the distinction 
between Proof and Inference (the only other process with 
which Proof is liable to be confounded), the next point of 
preliminary interest appears to be the subject-matter on 
which Proof is employed. I say of preliminary interest, 
because on the plan to be here adopted, we need in this 
place attempt to treat only a very small group selected 
out of all the complicated questions, so important and 
so fundamental in the higher study of Logic, centering 
in the doctrine of Proposition, or Assertion, or Judg- 
ment. For we are not concerned in any direct way with 
the Psychology of either Perception, Thought, Judgment, 
or Inference : Proof is concerned with ready-made Asser- 
tion only. At present we have only to notice certain 
broad distinctions in kinds of Assertion, with especial 
reference to the bearing of these distinctions on the 
question of Proof. A judgment is a Thesis only when 



42 . FALLACIES. [Pabt I. 

capable of expression in intelligible language, and while 
the need for Proof is felt. 

First in importance for us is the distinction between 
Real and what may be called Unreal propositions. The 
latter of these are insusceptible of Proof : the former are 
its subject-matter. 

The name 'Unreal' as here applied to propositions, 
is somewhat wider than what is usually meant by 
- verbal.' Usually the distinction between real and 
verbal is taken to correspond precisely to that between 
1 accidental ' * and ' essential ' propositions ; verbal pro- 
positions being restricted to mean such only as are 
tautologous or identical, — those in which the Subject f 
already contains, as a part, at least, of its meaning, that 
which is asserted of it in the remainder of the proposi- 
tion. Thus, ' A triangle is a three-sided figure ' is com- 
monly given as a typical example of the verbal proposition. 
But for our purposes we need some name to express indis- 
criminately all kinds of assertion which are insusceptible 
of Proof ; and in order to avoid ambiguities I propose to 
call these ' unreal,' rather than verbal. In itself the name 
1 verbal ' might certainly be held to designate very appro- 
priately every proposition which is merely a string of 
words, fulfilling, it may be, all grammatical requirements, 
but without conveying sense, — mere empty sound so far 

* Or, as the corresponding ' Judgments ' are termed (by Hamilton and 
others), ' Ampliative ' and ' Explicative,' or (by Kant) ' Synthetical ' and 
' Analytical.' 

f ' Subject' we may define provisionally as ' that which is primarily 
spoken of.' There will be more to say about it presently. 



Chap. II.] SUBJECT-MATTER OF PROOF : IN GENERAL. 43 

as possibility of interpretation is concerned ; but ' verbal ' 
is a name already in use for a more restricted purpose. 

At this stage it is not necessary to face the question 
as to the means of distinguishing in practice unreal pro- 
positions from real. Such inquiry belongs to a later 
place in our scheme, and will there be to some extent 
discussed.* At present, we have only to register the 
fact that unreal propositions are to be met with, — empty 
shells of assertion without a kernel, — and to set out the 
heads under which these may be conveniently divided. 

In the first place, then, comes the case, already spoken 
of, where the assertion is already made as soon as the 
meaning of the 'Subject' is understood, — tautologous, 
or essential, or identical propositions. It is easy to see 
that where that which is said of a thing is that which is 
known already, or rather that which is already told as 
soon as the Subject is enunciated, the proposition (for in 
form it may still of course be a proposition, containing 
nominative case and verb) lacks, if not raison d'etre, 
at least capacity for proof. The mere attempt to prove 
any such proposition involves a vicious circle in our 
thoughts. We have prejudged already, by hypothesis, 
the question of its truth, and inquiry can lead but to one 
result — a result which might have been reached without 
the labour. If, for example, a coroners jury were to give 
it as their solemn opinion, that 'deceased came to his 
death by extinction of the vital forces,' it would require 
no great effort to see that this supposed piece of informa- 

* See pp. 120-147. 



44 FALLACIES. [Part I. 

tion leaves us exactly where we were before. This, 
however, is rather an extreme instance. Perhaps the 
commonest case of all is where, in some shape or other, 
a proposition laboriously informs us that excess is not 
advisable, — as (in a discussion on local legislation in one 
of the Channel Islands, — I quote from a newspaper 
report) " The Bailiff said, it was essential that no measure 
should be unnecessarily adopted. On the other hand, 
everything necessary must be done." Or again, " I should 
not advise too great hurry," or "Growing lads and 
women should not attempt too much at a time." If ' too 
much ' means anything at all, it means that on the whole 
the amount spoken of is not advisable, and in all such 
cases no real information is given until the speaker pro- 
ceeds to say how much is considered by him excessive.* 
These instances are purposely chosen as being almost 
self-evident and indisputable. Later on,f we shall have 
occasion to notice some of the real difficulties in the 
matter. 

In the second place come the cases where the asser- 
tion made is already denied in the meaning of the Subject 
— self-contradictory, or suicidal propositions. These, of 

* It must be here remarked, however, that in many cases such asser- 
tions are merely blundering expressions, or grammatical solecisms, rather 
than absolutely without a meaning, — the speaker and his audience both 
having some actual amount dimly in view. There are also, no doubt, a 
few cases where ' too much ' does not really intend to sum up the total 
question of advisability, but refers to some other standard, as in the 
sentence, 'It is better to have too much luggage on a journey, than 
too little.' 

t See p. 124, inf. 



Chap. II.] SUBJECT-MATTER OF PROOF : IN GENERAL. 45 

course, stand essentially on the same footing as the class 
just mentioned. The question of their truth is prejudged 
already, only the reverse way. Perspicuous examples 
which are really faulty are less common here however, 
since the explanation of their actual employment is not 
so frequently as in the case of tautology a slipshod, 
do-nothing, easily satisfied habit of thought, but rather 
a youthful, reckless, revolutionary spirit, making use of 
poetical license in expression, or aiming at strong 
rhetorical effect. There is usually more life in self- 
contradictory assertions than in platitude, even if it be 
life of a rather uncurbed nature, and often these are used 
to convey in a forcible, epigrammatic manner, real truths 
which may indeed be paradoxical (in the sense of being 
contradictory to received opinion), but which are none 
the less worth knowing : still, as they stand, such propo- 
sitions take their place outside the realm of Proof, since 
in Logic we are necessarily limited by language, what- 
ever its faults may be. Luckily, however, an epigram 
that is worth anything may generally be translated into 
a real proposition if we can be content to sacrifice its 
merely artistic qualities ; and since the practical value of 
these can only be for stirring up our sluggish attention, 
when this object is once accomplished we may safely 
relapse into a cooler state of mind. Where harm is done 
by self-contradictory propositions is not so much in the 
field of positive assertion as in that of doubt; where, 
for instance, doubts are nominally raised, by means of 
language, about something which language itself postu- 



46 FALLACIES. [Part I. 

lates as a starting-point, — as (e.g.) " Can one individual 
be at the same time another individual ? " Or, " By 
successive additions of nothing, can something be at last 
developed ? " No question here can exist for Proof, as 
we shall understand that term, since the answer is 
given already in the postulates of language (otherwise 
known as the ' Maxims of Consistency ' or the ' Laws of 
Thought'*), and language is needed in order to state 
the question. 

This remark leads us to the outskirts of a very thorny 
subject, — namely the position of 'Ultimate beliefs' in 
regard to unreality. It may be said at once that they do 
not come within the subject-matter of Proof as here 
understood. Without attempting to determine, even 
approximately, the number or the nature of these ulti- 
mate beliefs, or to say anything further about them, it 
will suffice to acknowledge (if required to do so) that such 
there must be. Pushing back the examination of reasons 
for any belief we must of course either ultimately come 
to a basis of mere assumption, or go on questioning for 
ever. It seems best, therefore, at once to admit the 
existence of beliefs which may stand above, and not 
below, the possibility of 'Proof;' and then to relegate 
all discussion of such beliefs and their validity to those 
who feel desirous of examining them, and competent to 
undertake the inquiry. For us, in the mere capacity 
of logicians, and not metaphysicians, language limits 
thought ; and we therefore start at least with the Postu- 

* See also pp. 14, 105. 



Chap. II.] SUBJECT-MATTER OF PROOF : IN GENERAL. 47 

lates on which the meaning of language depends, dispens- 
ing with all attempts to climb outside or above them. 
Only so far then as a real meaning can be found in the 
answer Yes or No to any question, — a meaning expressible 
in consistent language and translatable, if need be, into 
terms of practice, — will such question come within our 
subject-matter. Wherever to doubt any belief, — e.g. that 
'whatever is, is;' or that 'it is impossible for the same 
thing at once to be and not to be ' — would nullify the 
postulated meaning of the language used, such belief (if 
it can be called a belief at all ; but this may be conceded 
for the sake of peace) we will consider to lie above the 
possibility of proof. And wherever this does not appear 
to be the case then the grounds of the belief will be 
open to our examination, even if for the purpose of 
saving time or trouble it may be also open to us to dis- 
pense with such inquiry. The view appears a tenable 
one, and has been stated at some length by Mr. Spencer,* 
that certain supposed questions, commonly believed to be 
of metaphysical interest, cannot be strictly called ques- 
tions at all, in any fruitful sense of that term : but since 
controversy is not here an object, it seems simpler to say 
that we choose to limit our own inquiry as above. 

Thirdly comes the case where any term used in a 
proposition fails, whether through self-contradiction t or 
otherwise, to convey intelligible meaning. There is, so 
far as I am aware, no special name in use for this kind of 

* Principles of Psychology, pt. vii. ch. iii. 

t i.e. within the term, not between the two terms. 



48 FALLACIES. [Part I. 

unreal assertions as a class, although certain forms of 
them have (very properly) earned the name of mysteries. 
These too, from the nature of the case, may safely sing in 
presence of the robber Doubt. So far as they are consist- 
ently incomprehensible, so far the question of their truth 
or falsity can clearly not be raised, except in words. Their 
acceptance, indeed, as a formula, may show a willing and 
tractable spirit, and they may to that extent have a 
value : but such acceptance differs of course from belief 
in being admittedly a voluntary act, and not a mere im- 
meritorious and reluctant yielding to the brute weight of 
evidence. Here too it is somewhat difficult to find 
examples which shall be universally perspicuous, — unless 
we take such questions as were sometimes discussed by the 
Scholastics, — as whether two glorified bodies can occupy 
the same portion of space at once, or whether God knows 
more than He is conscious of: or the doctrines of the 
Cabbala, — that all souls pre-existed in Adam, that the 
human is united to the Divine mind as the radius of a 
circle to its centre, or that existence is infinitely distant 
from non-entity. 

Besides assertions which are thus completely insus- 
ceptible of Proof, there are also many cases where Proof 
may appear to be inapplicable; which cases however 
must be carefully distinguished from unreal propositions. 
Such, for example, is the case where, though the belief is 
real enough, and quite possibly sound, proof is unattain- 
able owing to the multitude or the intangible nature of 
the grounds of belief, or owing to the shortness of the 



Chap. II.] SUBJECT-MATTEK OF PEOOF : IN GENERAL. 49 

time available for their examination — as where we take 
a violent liking or dislike to a person at first sight, or 
have to decide in a hurry upon some complicated course 
of action. In such cases the incapacity for proof — if 
there be real incapacity — cannot be discovered by mere 
inspection of the thesis, but needs to be shown by ex- 
ternal evidence. And unless and until this is shown in 
the given case, we have clearly no reason to treat it 
differently from any other real assertion. 

Under the head of propositions insusceptible of exact 
proof it may be well also to notice that immense class of 
assertions, very commonly in use, whose essential nature 
is to. be vag ue. Such assertions as that on the whole the 
ordinary meaning of a word is so and so, or that there is 
a growing tendency among civilised people to do this or 
the other ; or, still more, the finer shades of suggestive, 
tentative assertion conveyed in poetry, jest, or innuendo : 
these afford, from the nature of the case, an insecure 
footing for the fruitful application of logical method. 
But these, too, stand on a very different level from unreal 
propositions, since the reduction of them to definiteness is 
not in any way precluded by their own postulates, but 
only difficult perhaps, or at any rate inconvenient on 
some ground or other. When we meet with one of these 
assertions, two courses are open: either to treat it in 
a spirit of generosity or carelessness, accepting it as 
claiming only a lower degree of assertive force, and as 
fulfilling its own purpose if not exactly ours ; or else, if 
exactitude be for any reason really important, expending 



50 FALLACIES. (Taut I. 

the trouble necessary to render it as far as possible 
definite. Until this is done there is of course room for 
misinterpretation, and therefore no security for strict 
sifting of the question raised. 

Lastly, it is obvious that many assertions which might 
be proved, do not in fact stand in need of it. There are 
a vast number of cases in which Proof is practically never 
demanded. That ' Socrates is mortal/ for example, or 
that 'Queen Anne is dead ;' that ' some coins are metallic/ 
or some logical examples rather absurd; these are assertions 
which, for all practical purposes, may now be considered 
sufficiently safe against serious attack. Here, too, no 
general rule can be given for distinguishing propositions 
which have been sufficiently proved already from those 
which still stand in need of proof. This is one of the 
matters which fall quite outside the scope of Logic, and 
must always be decided between the assertor and his 
audience by special agreement. It is, in fact, merely pre- 
liminary to Logic, and in no way connected with the 
actual methods of Proof. To claim for a proposition, the 
truth of which is still highly doubtful, the advantage 
which belongs to one that has successfully resisted all 
attacks, is no doubt a common enough rhetorical device. 
So, on the other hand, is the attempt to obstruct an 
argument by raising unnecessary difficulties. But Logic 
cannot undertake to judge of motives. Later on, in 
speaking of the Burden of Proof, we shall have occasion 
to notice this difficulty more fully.* At present it is 

* See pp. 154-167, inf., also pp. 128, 171. 



Chap. II.] SUBJECT-MATTER OF PROOF : IN GENERAL. 51 

important to pass on to the discussion of Heal Assertion, 
its nature in general; and to a broad classification 
of the kinds of Real Assertion that may be proposed 
for Proof. 



II. Subject and Predicate. 

It is on all hands admitted that every proposition, as 
soon as understood, may be divided into two parts — the 
subject, or name of the 'thing' primarily spoken of, and 
the remainder of the sentence, or the words expressing 
the whole assertion made about such Subject. If we de- 
note the Subject, as is usual for shortness, by the letter S, 
we may denote the remainder of the proposition by the 
letter J — the Judgment made about the S. 

In so general a science as Logic — or since the province 
of Logic is not yet clearly marked out, let us say in so 
general a science as that of Evidence, or Proof — we find 
ourselves constantly brought up against the difficulty of 
obtaining words wide enough to include all that we 
mean. Thus, though assertion always asserts 'some- 
thing' of 'something' else — though 'everything' may 
have assertions made about it — yet it seems hardly safe 
to say that assertion is always about ' things ; ' unsafe 
at least without explaining that ' thing ' is here used in 
the widest possible sense. Not merely every thing (as 
commonly understood — namely every material object) 
may be the S of a proposition, but literally everything, 
or anything, that can be named at all : everything that 



52 FALLACIES. [Paet I. 

can be spoken of, whether objective or subjective, real or 
imaginary, whole or part, great or small. The universe 
itself is a ' thing ' in this sense, and so is every portion 
of it. Time and space are things in this sense, and so 
is the year 1882, or the point of the pen with which I 
write : so is the heat of to-morrow's sun, or the justice 
shown in my friend's remarks of yesterday : so is the 
word ' Logic,' or the meaning of that word, or the 
relation between its meaning and something else, or the 
character of that relation, or the fact that the character 
of that relation is beyond my power to state. We need 
some name thus to express in general ' anything that 
may be spoken about,' and in spite of the possibly mis- 
leading associations of the word here chosen (which at 
first sight may seem to demand tangibility almost, or at 
least visibility or weight) there is really no other name 
that will mislead so little. If we may say 'every- 
thing ' in one word shall we not say ' every thing ' in 
two ? At any rate such employment of the word will 
here be postulated, in default of any other name to serve 
the purpose required. 

Every proposition, then, so soon as understood, may 
be divided into S and J. But it may also be divided in 
this way before the proposition as a whole is clearly 
understood : namely, as soon as S alone is distinguished, 
and while the complete assertion made is still obscure. 
J itself is subdivisible, and until this further subdivision 
is ready to be made, the meaning of the proposition is 
not yet completely apprehended. 



Chap. II.] SUBJECT-MATTER OF PROOF : IN GENERAL. 53 

Mr. Yenn, in his Symbolic Logic* discusses three 
distinguishable views of the import of propositions — the 
'predication view, the class inclusion and exclusion view, 
and the compartmental view; finally adopting the last 
as best suited to the purposes there aimed at, and espe- 
cially to the solution of intricate artificial problems. But 
there is a fourth theoiy which, though agreeing with the 
compartmental view in one of the main points in which 
it differs from the older doctrine — namely in considering 
that every proposition has (at least) two subjects, each 
term being the name of a " thing spoken about " — yet 
seems to me to differ from it fully as much as the pre- 
dication-view and the class-view differ from each other. 
That theory, suggested in Mill's system,f stated very 
broadly by Mr. H. Spencer^ and more recently worked 
out into considerable detail by Mr. Carvcth Read,§ may be 
described as the relation-view of propositions, and may be 
briefly explained as considering that every proposition 
really asserts the manner in which two 'nameable 
things' are related to each other; e.g. as resembling or 
differing, and to what extent; as successive or simul- 
taneous in time, or conjoined in space, and whether 
invariably so or otherwise. For example, the most im- 

* Chap. i. 

t In spite of Mill's express adoption of the predication-theory 
(Sysiem of Logic, bk. i. ch. iv.), yet his whole view of 'connotation,' as 
also of causal sequence, was essentially that of a relation asserted 
between two Subjects. 

X Principles of Psychology, part vi. chap. viii. 

§ Essay on The Theory of Logic. 
4 



54 FALLACIES. [Part I. 

portant assertions of succession in time are those of 
Causation, — the effect following its cause : again, descrip- 
tive assertions, and those which classify the S, may always 
be viewed as asserting the conjunction of attributes (in 
space or time or both), — as when the attribute 'falli- 
bility' is said to be invariably conjoined with the other 
attributes common to human nature. 

It is usual in Logic to divide what was above sym- 
bolised by J into (1) Copula, and (2) Predicate : and if it 
were possible to keep these names while avoiding 
ambiguity, I would gladly do so. But though ' Copula ' 
might fairly be used to express 'relation asserted/ it 
seems impossible to divest the name c Predicate ' of its 
etymological associations, so as to view it as really the 
name of another c thing spoken about.' We must there- 
fore here adopt another symbol, and perhaps the letter £o 
is as little ambiguous as any. Under the relation-view 
then, the form of proposition would be, not S copula P, 
but S copula g^. 

In adopting the relation- view, however, it must by 
no means be supposed that we need therefore discard the 
traditional doctrine as erroneous. The predication-view 
is useful for many purposes, and perhaps its best practical 
excuse is that so often one of the two ' things spoken of 
is more directly spoken of than the other. One of them 
forms the starting-point for the assertion, while the other 
forms its goal. Thus S may denote an observed or known 
event, and £& its supposed cause or effect; as in 'This 
death points to foul play,' or ' The war will disturb all 



Chap. IL] SUBJECT-MATTER OF PROOF : IN GENERAL. 55 

prices:' or S may be the name of something quite 
familiar, and g& one of its less obvious causes, conse- 
quences, or concomitants, or less familiar names; as in 
'Tubercle is due to organic germs/ or 'Strikes are 
ruinous to the country,' or 'Gold has specific gravity 
19 '34,' or 'Whales are mammals.' Although, in short, 
every relation is, strictly speaking, two-sided, not every 
assertion is concerned equally about both its possible 
aspects. If S 'resembles' Jb, for example, it certainly 
cannot be denied that the latter also resembles the 
former, and yet our whole concern in making the asser- 
tion may be to bring the former just within the range 
of what we know (or suppose to be true) of the latter ; 
our knowledge of §b, as regards relation to a third 
term, Z, being in some way better established than our 
knowledge of S. Again, if S 'indicates' §fe, the latter 
'is indicated by' the former; but the main purpose of 
indication is, of course, to point from sign to thing sig- 
nified. The former is the starting-point and the latter 
the goal. 

The relations that may exist between S and Jfc, as 
thus understood, are of course extremely numerous. 
That is to say, we can, if for any purpose it be desirable, 
distinguish an endless number of them. S may, for in- 
stance, be the father of *», or his mother, child, wife, 
etc.; or larger than §fe, or less ambitious, or may live 
next door to *>, or may be related to him, or her, or it, in 
a million different ways. For our purpose, however, it 
will fortunately be sufficient to make only the broadest 



56 FALLACIES. [Part I. 

subdivision; and such subdivision will be the subject of 
the next following chapter. But first there is a prelimi- 
nary source of difficulty to be cleared away. 



III. Simple and Complex Propositions. 

Such propositions as, 'All men are fallible/ or 'He 
is a man/ are somewhat unusually simple. That is to 
say, they are capable of being expressed in comparatively 
few words, without either circumlocution or intricacy. 
There are, indeed, other propositions still simpler, as ' He 
runs/ or 'I exist;'* but the majority in common use 
are of a much more complicated nature, each of the 
terms being frequently made up of a large number of 
words, or even of a combination of intricately inter- 
woven clauses. This sentence just written, for example, 
is only moderately advanced in the scale of complexity, 
and yet considerably more so than 'All men are fallible:' 
any book or newspaper taken at hazard will immediately 
supply the reader with a dozen better instances. Simple 
propositions, of the type so familiar in logical text-books, 
are quite exceptional in real life. 

From our point of view there is no firm line to be 
drawn between simple assertions and complex ones. 
That is to say, so soon as we distinguish the terms of 
any proposition, no matter how complex in verbal form, 

* For the manner in which propositions asserting mere existence of 
the S may be viewed as stating a relation between two terms ; see Bain' a 
Logic, book i. chap. iii. § 23. 



Chap. II.] SUBJECT-MATTER OF PROOF : IN GENERAL. 57 

we thereby simplify it into one assertion. The mere 
fact that a given set of words can be viewed as com- 
prising two assertions coupled by a 'conjunction/ does 
not necessarily prevent us from taking the two together 
and considering their joint intention. Still less, of course, 
do mere dependent clauses, or adjectival or adverbial 
limitations, destroy the unity of meaning. The com- 
monest type, perhaps, among propositions is that where 
the terms each consist of some main constituent, limited 
or qualified in several ways. It is rarely that we have 
the opportunity of making a perfectly simple statement 
about a ' thing ' which can be expressed by a perfectly 
unqualified name, — as 'man' or ' humanity :' we find 
it safer as a rule to confine the extent of our assertions 
somewhat, and thus we render them complex in form. 
There are comparatively few statements that we can 
make with any safety about ' All men/ except such as 
are already too familiar to be much required: but we 
may often find occasion to speak of 'All men who 
possess such and such a peculiarity/ or ' All except those 
who, etc./ whereby our sentence becomes more complex 
and the assertion more limited in range. 

It will not be necessary here to make any division 
of propositions in order to show the different kinds of 
complexity to which they are liable. Such a question is 
altogether more of grammatical interest than logical, and 
has certainly no importance for any purpose here under- 
taken. As will be seen later, we postulate agreement 
as to meaning, as a starting-point for Proof, declining all 



58 FALLACIES. [Part I. 

invasion of the grammarian's province by any attempt 
to decide authoritatively what any given form or set of 
words shall imply. But it seemed necessary to make 
clear from the outset that the number of words, or of 
phrases anyhow combined, is, in our view, in itself no 
bar to the whole group being regarded as one assertion. 
Thus (e.g.) the complex assertion, ' He is fallible, for he 
is a man,' besides being capable of being viewed as tivo 
propositions set in relation to each other by a conjunctive 
particle, is also capable of being viewed as itself one 
whole proposition ; * i.e. as being divisible into two terms 
set in relation to one another by means of a copula. But 
this will appear more clearly in due course. 

• See also pp. 34, 100, 310, below. 



CHAPTER III 

THE SUBJECT-MATTER OF PROOF : MAIN KINDS OF 
THESIS. 

L Indication. 

The most general of all relations, asserted or denied, 
is that which for want of a better name may in the 
meantime be called ' Indication.' The copula ■ indicates/ 
as here understood, includes the copula ' is ' (as in ' S is 
P '), stretching, however, beyond the usual interpretation 
of the latter. By calling this the most general relation 
it is meant that, with the one doubtful exception of the 
purely quantitative relations (the laws of which are amply 
developed in Mathematics, and require notice only in a 
more comprehensive scheme than can here be attempted), 
every proposition may be viewed as saying that one 
thing ' indicates, or does not indicate, a certain other. 

The apparent rashness of this statement will serve at 
least to show where the difficulty lies. Some word is 
wanted, for the purpose of generalising, in one expression, 
several kinds of assertion which are commonly described 
by different names ; no word appears to me to be better 



60 FALLACIES. [Part I. 

suited for the purpose than ' indicates/ and yet even this 
would certainly not be sufficient without some explana- 
tion. By means of the symbol — >, indeed, it is possible 
to avoid ambiguity, but since the symbol must have a 
name we cannot altogether escape the use of language, 
and can only strive while using it to avoid any misleading 
associations. 

For the purpose of dealing with the dangers of Proof, 
— including thereunder all dangers to which a thesis, or 
asserted judgment, is liable, — the most important fact 
about propositions seems to be the power which they 
give us (when their truth is believed) of passing from 
the known to the unknown. There are two distinct 
ways in which they may do this, one of which may be 
called ' implication,' * and the other ' material indica- 
tion;' the former being the case where by merely 
analysing the meaning of a name or proposition we 
either arrive at or guarantee certain of its less obvious 
consequences; while ' indication' (in general) includes 
this case and also the commoner one where we obtain 
the same power, not by mere analysis of the meaning, but 
by viewing one fact as material evidence for another, 
— evidence asserted as strong enough to stand against 
all hostile criticism. The proposition 'Man is fallible' 
might be an instance of either of these modes of indica- 

* Cf. Mr. H. MacColl, in Mind, No. xvii. p. 45. The difference 
between Mr. Mao Coil's view and mine appears to me far less important 
than the resemblance ; and I trace mnch of my own view (and especially 
the 'law of connter-indication ') jointly to the article quoted, and to 
Wundt's reoent work (Logik, vol. i. Erkenntnisslehre). 



Chap. III.] MAIN KINDS OF THESIS. 61 

tion, according as the notion ' fallibility ' did or did not 
enter into the special meaning postulated for the name 
' man.' If we pass to ' new knowledge ' * by analysing 
the old, we do not reach a new theory, but the applica- 
tion of an old one : while the attempt to prove by way of 
implication is, of course, either to argue in a circle or to 
appeal ad hominem. Material indication is the sole 
means of really passing from unknown to 'theorised/ 
or from theorised to known, — so far as knowledge is 
capable of being guaranteed. 

The chief difficulty about the name 'indication' consists 
in stretching it to cover the assertion of both Law and 
Fact; or, as such assertions will here be called, Abstract 
and Concrete propositions. It is easy enough to see how 
every Law asserted may be viewed as an indication, since 
the primary purpose of every law is, of course, to be in- 
terpreted, or applied : hence the S of every abstract pro- 
position is expressed either directly as a ' general name ' 
(simple or complex), or else, — and especially where such S 
is itself a proposition — is generalised by means of an ' if,' 
or ' where,' or ' when,' etc. But when we come to speak 
of concrete propositions, the word ' indicates ' draws us 
at once into clumsiness of expression. This case of 

* The question whether, by analysis merely, we can " increase our 
knowledge" is as ambiguous as the question whether by digestion we 
can " increase " the food we swallow. We do not increase its sum, or 
weight : we do increase its utility. We get a new and firmer grasp of 
old material. Though we may, of course, add to our power of applying 
knowledge, by analysing accepted truths, this merely points to the 
thoughtlessness with which we habitually bolt our axioms whole. 



62 FALLACIES. [Part I. 

death, no doubt, may indicate (or point to) poison, or my 
pulse at the present moment may indicate (or show) the 
absence of fever, or yesterday's panic in the city may 
indicate (or foreshadow) a future increase of bankruptcy ; 
but it is undoubtedly clumsy to say that Bavius ' indicates 
the qualities of a fool: we habitually condense those 
four words into the one word ' is.' 

Nevertheless, with this apology, I propose to use the 
name ' indicates' in default of a better to fit all cases. 
Much of the difficulty may be removed by remembering 
that it is only in abstract propositions that S is really a 
sign, in the ordinary sense of the term : it is only there 
at least, that it is intended to be used as a sign, or mark, 
or label, bearing a recognised meaning. The essential 
characteristic of concrete propositions is that their S 
cannot be said, in general (i.e. universally) to indicate 
the §b, except by virtue of all the special circumstances 
bound up along with the thing most prominently denoted 
there as ' S.' It may, indeed, be on general grounds 
only that we believe this or that concrete proposition, — 
as, that ' the panic will increase the number of failures : ' 
but this does not appear in the statement. In the con- 
crete proposition we distinctly assert the possession of 
something over and above mere general grounds, namely 
a full review of all the special circumstances. In spite of 
any hidden facts, we assert our judgment as deserving of 
belief. 

The assertions which are thus to be included under 
the symbol — > (which may be read ' indicates') are 



Chap. III.] MAIN KINDS OF THESIS. 63 

accordingly those of Dependence * (whether causal or 
logical) and of Classification. By an assertion of causal 
dependence is meant an assertion that two ' things,' — 
usually events, but sometimes objects or qualities, — are 
causally connected so that one of them is to some extent 
an indication of the other, whether a sign in the strict 
sense, or merely a symptom. Some ' things ' in nature 
are found, or supposed, to be marks or signs of others, 
as a falling barometer indicates a coming storm, or as 
breathing indicates that life is not extinct, or as every 
existing human being indicates the prior existence of 
a pair of human parents. The statement of these indica- 
tions may accordingly be written : ' Falling barometer 
— > coming storm/ ' Breathing — > presence of 
life' and 'Human being — > prior human parents.' 
By an assertion of logical dependence is meant an asser- 
tion that the truth of one proposition ' follows from ' 
that of another, or that the meaning of one name is 
included in that of another. Most names and propositions 
are intended to bear a meaning, — that is, to mark or 
signify notions or facts, — and some propositions are 
intentionally put forward as guaranteeing the truth 
of others. Thus the name ' Intolerance ' may be in- 
tended to include the notion ' active hostility ; ' or the 
assertion ' He is coming,' the fact ' He is not here ; ' or 
again, the assertion ' He is a man ' may be employed to 
guarantee the truth of the assertion ' He is fallible.' And 
these may respectively be written 'Intolerance — > 

* Cf. Wundt. Logik : Erlenntnisslehre, pp. 179-186, 277, 281, etc. 



64 FALLACIES. [Part I. 

active hostility/ 'He is coming — > he is not here* 
(but of this the usual grammatical form would be ' If, or 
since, he is coming he is not here/) and ' He is a man 
— > he is fallible ' (or ' He is a man, and therefore he 
is fallible ; ' or ' He is fallible, for he is a man/) By an \ 
assertion of Classification is meant the extremely frequent j 
cases where a ' thing ' is said to deserve a certain name, / 
or to bear ' essential resemblance ' to another thing, or 
to belong to a certain class, or to possess a certain quality, 
or to have another thing 'coexisting' with it; as in 
'Gold is an elementary substance/ or 'belongs to the 
class elements/ or ' The State essentially resembles a 
family/ or ' Every rose has its thorn ' (or ' With every 
rose a thorn co-exists ') ; which may accordingly be 
written 'Gold — > Element/ 'State — > Family/ 
' Rose — > Thorn.' 

II. Affirmation and Denial. 

Indication may be either affirmed or denied. Certain 
propositions, instead of committing the assertor to any 
definite statement of the relation between S and £b, 
are content to say merely that some definite assertion, 
taken as already made about them, is untrue. These 
will be called Denials : all others will be called positive 
Assertions, or ' Affirmations.' 

It is a matter of some difficulty to mention any 
special grammatical form as fairly representative of the 
denial, since even sentences containing the negative 
particle 'not/ in close connexion with the verb, or the 



Chap. III.] MAIN KINDS OF THESIS. 65 

quantification ' no ' before a noun, or a ' negative name ' 
as P (or £&), are very frequently used to express a posi- 
tive assertion as here defined. Thus we may say, ' That 
is not bad/ or 'No pen can attempt to describe the 
scene/ or ' He is unskilful, worthless, disagreeable, incom- 
petent, etc.,' without at all attempting to confine our- 
selves to bare denial of something either actually or only 
presumably said before. The grammatical form of the 
proposition, though often useful as a hint towards the 
meaning in this respect, is at best an uncertain guide ; 
nor can even the whole context be taken as in every case 
complete evidence of the real intention. 

The two distinct intentions do, however, exist, and 
are to some extent inferrible from the words employed. 
Where the intention is doubtful, there is nothing to fall 
back upon except an express declaration by the speaker 
as to the sense in which the proposition is put forward. 
At present, however, we are not concerned with the 
means of arriving at the intention, but only with 
classifying those distinguishable meanings which have 
importance for the doctrine of Proof. Of these the 
most important is the distinction between positive 
assertion and bare denial. And having called attention 
to this fact, we may proceed at once to examine more 
in detail the manner in which this distinction runs 
across the othern. 



QQ FALLACIES. [Part I. 

III. Abstract and Concrete Propositions. 

Next in importance is the opposition between Law 
and Fact asserted; or, as it may be otherwise called, 
between Abstract and Concrete propositions.* 

The abstract proposition may be expressed indiffer- 
ently in any one of various grammatical forms, of which 
perhaps the commonest are those familiar types (denoted 
under the traditional scheme by the letters A and 
E) whose S is the name of the members of a class, 
' All ' or ' None ' of whom ' are ' P. Thus, ' All men are 
fallible' (A), or ' No men are secure against fallacy' 
(E), are simple, straightforward examples of the asser- 
tive abstract proposition. In both cases the attribute 
'humanity,' wherever found, is said to indicate the 
attribute ' liability to error.' Another common form 
which the abstract proposition takes, is where the S con- 
sists of what is sometimes loosely called an 'abstract 
name,' as ' honesty ' or ' theft.' Thus, we might assert 
that ' Honesty is the best policy,' or that ' Theft cannot 
prosper long;' meaning, in the two cases respectively, 
something rather more clumsily expressible by ' Honest 
actions, in general, indicate success as likely to follow,' 
and 'Dishonest actions, in general, indicate that (in 
spite, it may be, of temporary success) ultimate failure 
is probable.' Of course, these and similar sentences 
may contain other meanings also — may even be used 

* Cf. also " noticral " and " real " propositions in Newman's Grammar 
of Assent, p. 7. 



Chap. IIL] MAIN KINDS OF THESIS. 67 

ironically, — but in so far as they are used to express 
the meaning explained, to that extent they are what 
we here call assertive (or affirmative) abstract proposi- 
tions. Again, the adverbs ' always ' and ' never ' are 
very largely used to express the copula of assertive 
abstract indication, as in ' Bread always falls upon the 
buttered side/ or ' A story never loses by re-telling.' And 
again, another still commoner grammatical form in use 
is the conditional or hypothetical sentence, beginning 
with ' if,' or ' when,' or ' where,' or ' while,' etc. ; as in 
1 If it rains in Ceylon, it pours,' or ' When poverty comes 
in at the door, love flies out of the window,' or ' Where 
there is smoke there is fire,' or ' While there is life, there 
is hope : ' in each of these cases the purpose of the 
proposition may be to assert of one 'thing' that it 
universally indicates another, whether in the past, 
present, or future, relatively to itself. We need not at 
present follow these grammatical variations into further 
detail : enough has been said to illustrate them in a rough 
preliminary manner. 

The concrete proposition, on the other hand, contents 
itself with a less (apparently) sweeping assertion. It says, 
not that S wherever found indicates §9, but that in this 
particular instance it does so. Looking at all the cir- 
cumstances the present dearness of money indicates a 
coming panic, the circumstances of this man's death point 
to some kind of poison, the latest political movement 
indicates dissension in the cabinet, or deserves the name of 
revolutionary or reactive, or whatever else it may be. 



68 FALLACIES. [Part I. 

The difference is perhaps best expressible by saying that 
while in the abstract assertion S is spoken of (but by no 
means really conceived) apart from any circumstances 
which may serve to individualise it, in the concrete 
assertion the reverse is the case : we here say that talcing 
all special circumstances into account, this S indicates 
§b. It is true that to every concrete fact of causation 
there must correspond a law, if we can discover it ; but, 
practically, most laws abstract more or less from the 
circumstances of the concrete. 

Corresponding to abstract assertions there are abstract 
denials ; and of these, two kinds may be distinguished. 
Sometimes we deny a law by asserting that there are 
exceptions to it ; sometimes {e.g. frequently in classifying 
or name-giving propositions) by asserting that it totally 
fails ; or, in other words, that ' some difference exists 
between S and %b.* The former kind of denial may be 
called exceptive; the latter an assertion of difference. 
For the copula in exceptive propositions we shall hence- 
forth use, on occasion, the symbol -J— >, and for assertions 
of difference the symbol ^. 

As to exceptive denials, perhaps the most frequent 
grammatical form which these take is that known under 
the traditional arrangement as the ' particular ' * pro- 

* Cf. Symbolic Logic, chap. vii. p. 161. The particular proposition, as 
actually employed, no doubt serves several other purposes also, notably 
that of registering our first vague grounds of Inference, as contrasted 
with anything deserving the name of grounds of Proof. Finding two 
' things ' frequently or even occasionally conjoined, we often begin to 
get upon the track of some law, and eventually we may rise thereby to 



Chap. III.] MAIN KINDS OF THESIS. 69 

position (I or 0) : e.g. * Some negroes are fairly intelli- 
gent/ or ' Some Mexicans are not habitual liars.' Again, 
the adverbs ' sometimes ' or ' sometimes not ' are fre- 
quently used in exceptive denials ; and again the expres- 
sions * so is quite compatible with S/ or ' S is by no 
means necessarily £•> ; ' and again, the expression ' all 
. . . are not/ as in 'All that glitters is not gold/ and 
various other forms, such as, for example, 'There are 
lawyers and lawyers.' Here also no form of words is by 
itself perfectly unambiguous : we need something else to 
show whether the proposition is really intended as asser- 
tive or as a bare denial. But on the whole, and roughly, 
the particular proposition may be taken as most nearly 
typical of this class. No useful distribution of any 
proposition into its component parts, it must be remem- 
bered, can ever be made until the real intention of the 
speaker is clear. 

As to ' assertions of difference/ there is some difficulty, 
as the name chosen may help to show, in placing 
them quite clearly in the class of mere denials. The 
justification for doing so lies, however, in the fact that 
without some supposed belief that, for the purpose in 
hand, no difference exists {i.e. that S — > §3) the asser- 
tion of difference is too trivial to have any practical 
value, since points of difference may always be found 
between two things, however nearly alike. Hence the 

the power of making, and perhaps proving, some abstract assertion 
regarding them. But, regarded as positive assertion, this is too vague 
to be called a ' thesis.' 



70 FALLACIES. [Part I. 

essential purpose of these assertions is to contradict some- 
thing already supposed to be believed. The sole practical 
use of the assertion of difference is either to break down 
a supposed analogy or to deny the applicability of a name, 
i.e. the right of a ' thing ' to belong to a certain class ; 
and this whether the proposition be abstract or concrete. 
Thus we might say * National Government is a different 
thing from family government' (abstract), or ' Whales 
are not fishes ' (abstract), or ' The Kilmainham arrange- 
ment was not a compact ' (concrete), or ' The case of Mr. 
A. is different from that of Mr. B.' (concrete). These 
propositions merely say that S differs from §b. For 
further examples of this form of denial we may take such 
expressions as ' Seeing is a very different thing from 
believing/ or 'Liberty is one thing and License quite 
another/ or even perhaps ' Force is no remedy ' ; though 
this last phrase has no doubt been more often used to 
express a vague law that ' Force — > probable continu- 
ance of the evil ' than merely to deny an assertion to the 
contrary or to correct the use of a name. As this last 
example may serve to show, there is sometimes a difficulty 
in deciding whether a given sentence is really an asser- 
tion that S indicates the absence of something (as ice, for 
instance, indicates the absence of a certain degree of heat), 
or a mere assertion of difference between S and §fe. But 
this is a difficulty which cannot be remedied by simply 
refusing to notice it. The possibility of misunderstand- 
ing the real intention of a given set of words, is one that 
can hardly too often be brought to mind. 



Chap. III.] MAIN KINDS OF THESIS. 71 

Corresponding to concrete assertions there are con- 
crete denials ; and of these again two kinds. We have 
already spoken, just above, of the concrete assertion of 
difference, and after what has been said of assertions of 
difference in general, the nature of the first kind of con- 
crete denial will be sufficiently clear. Nor is there much 
difficulty as to the other kind of concrete denial. It 
follows from the nature of concrete assertion that these 
cannot be at all described as ' exceptive/ since there is no 
law to which they directly take exception. Perhaps the 
best name for them is ' Simple denials.' These also are 
found in various grammatical forms, but the commonest 
is, no doubt, where 'not' is added to the verb, as in 
' This was not due to drink/ ' The crisis will not be fol- 
lowed by any important change/ ' It is not accompanied 
by much danger, after all/ etc. Also in this sense a nega- 
tive name as Jfc may be sometimes used, though perhaps 
rarely. Thus in saying 'The door is unfastened/ we 
might conceivably intend merely to deny the opposite 
assertion, but more probably the intention would be to 
convey a positive assertion of our own. When once the 
distinction between concrete and abstract propositions is 
clearly kept in view it becomes sufficiently easy to recog- 
nize the simple concrete denial. 

The abstract proposition is, then, the assertion or 
denial of any general law in Nature, of however narrow 
sweep or insecure stability : the concrete proposition 
is the assertion or denial of a single fact. The con- 
crete proposition takes a concrete S, ' this man/ ' these 



72 FALLACIES. [Paet 1. 

instances/ 'my lecture yesterday/ 'your hope of suc- 
cess ' and tells us what these ' indicate/ forwards in time, 
or backwards, or contemporaneously. And here must be 
noticed an objection which may possibly be raised at first 
sight to this use of the word ' concrete/ A man, it may 
be said, is clearly concrete enough, and so perhaps is an 
instance ; but a lecture, is not that dangerously near 
the abstract ? And ' Hope/ ' Success/ are not these 
purely abstract terms ? The answer is that no word 
(when used in a proposition — and it is only when so used 
that we are here concerned with words) is in itself either 
abstract or concrete, but its context makes it so. Any 
word may be either, according to the purposes of our 
assertion. We may speak of ' man ' or of ' men ' in the 
abstract, in spite of the solid flesh belonging to each 
individual ; and on the other hand, by hedging in a so- 
called * abstract name/ with the help of a demonstrative 
pronoun, or in whatever way the resources of language will 
allow us to apply such name to some actual concrete case, 
we destroy for the time its abstract nature, and the pro- 
position as a whole becomes concrete. If I make an 
assertion regarding the ' truth ' of some particular story, 
I state no law, and deny no law, but confine my remarks 
to one particular concrete fact. The underlying meaning 
of ' abstract ' is always ' detached from special circum- 
stances/ or ' generalised ; ' and so long ago as Berkeley's 
time our limitations in conceiving (or having a definite 
idea of) anything in the abstract have been clearly 
shown. We cannot conceive things in the abstract, but 



Chap. III.] MAIN KINDS OF THESIS. 73 

we can make abstract assertions regarding them; — can 
sometimes say, that is, how they will behave or how 
they should be explained or designated under all cir- 
cumstances indifferently ; and where we speak of this 
man, your hope, etc., we include special circumstances 
which ' man' and ' hope ' by themselves would lack. In 
the concrete proposition we sum up the total circum- 
stances, taking (or rather professing to take) all the indi- 
vidual peculiarities of the case into consideration before 
pronouncing judgment. Whether or not 'hope' in the 
abstract may tell nattering tales habitually, we say that 
taking all the present circumstances into account it does 
so here. The S of a concrete proposition differs from that 
of the corresponding abstract one in being saddled with 
all the individual peculiarities of the given case. And 
on this account the concrete assertion differs from the 
abstract one in being less easy to disprove ; since the 
' circumstances ' are nearly always wide enough to contain 
something that even science fails to reckon. 

It must now be sufficiently evident also that so long 
as the meaning is clear, the grammatical form of the 
sentence — categorical or hypothetical, simple or com- 
plex, A or E, etc. — is not of the slightest importance. 
The proposition, for instance, 'Murder will out/ is, for 
purposes of proof, the same whether expressed in this 
fashion or in the shape 'All murders are eventually 
discovered/ or 'No murders remain undiscovered/ or 
'Murder always comes to light/ or 'Murders never 
remain hidden/ or ' When (or if) murder is committed, 



74 FALLACIES. [Part I. 

detection is sure to follow/ or in whatever way it may 
suggest itself to rhetorical ingenuity to clothe the same 
meaning. At the root of all abstract propositions lies 
the formula — 

S (universally) — > £b 
and this whether §b be past, present, or future relatively 
to S and whether the name of either be positive or 
negative. In each case S (in general) is said to be a 
sign, or mark, of §■>, whether in the past, present, or 
future, relatively to itself. Where S is found, ^ (it 
is asserted) may be looked for. 

Abstract propositions play an important part in 
proof, — whether proof of other abstract propositions or 
of concrete ones. They summarise, in a compact and 
convenient form, whatever general knowledge of nature 
we have already obtained, and serve as tests to which 
to bring any new assertion propounded for proof. The 
establishment of these is of course the centre of interest 
for science. It is through the existence of such 'de- 
pendences ' that all explanation and prediction become 
possible, and our consistent recognition of them consti- 
tutes the main difference between our conception of 
Nature as a network of uniformities, and the earlier 
notion, so inevitable to savages, of a world governed by 
caprice or luck. 

Concrete propositions, on the other hand, although 
constituting in one sense the foundation for science, find 
their main interest, as subject-matter for proof, in a less 
exalted region. Although in common life also the truth 



Chap. HI.] MAIN KINDS OF THESIS. 75 

of general laws (more or less vague perhaps in their 
statement) may to no small extent be debated, yet the 
bulk of the questions arising there for settlement are of 
a concrete character; and, roughly speaking, the com- 
moner the life the more relatively frequent are the 
concrete assertions put forward. Whether this or that 
thing, person, or definite group, did act in such and 
such a manner, or does possess such and such qualities ; 
whether this or that individual action, event, or ' acci- 
dent' was due to such and such causes, or will have 
such and such results ; these are the most frequent ques- 
tions about which in daily life doubt arises, and which 
press for settlement and proof. Every one of these is 
concrete, — an assertion directly regarding individual 
fact, not general law, — and as such is marked off by a 
chasm as wide as any that can be made in Logic, from 
the propositions above defined as abstract. Between 
concrete and abstract knowledge, however, with respect 
to their attainment and growth, there has been mutual 
aid and mutual criticism so far back as can be traced at 
all. No doubt, in one sense, concrete knowledge (or some- 
thing separated from ' knowledge ' only by imperceptible 
degrees) is earlier in time, just as common life is earlier 
than Science. But in both there are now innumerable 
shades of development or completeness. It may be safe 
to say, perhaps, that from crude concrete perceptions the 
first predisposition for abstract knowledge arose, and 
that by means of such predisposition, aided by language, 
or signs, the first crude abstract guesses were formed. 



76 FALLACIES. [Part I. 

But the history of knowledge, from the earliest evidence 
attainable, is a record of the alternate and mutual pro- 
duction, correction, and illumination, of one kind of 
judgment by the other. At the present stage of pro- 
gress, as will be seen in speaking of the kinds of Proof, 
there are thus in operation two somewhat conflicting 
methods of testing truth, — two methods which, though 
often opposed as rivals, and either of which may at 
times become unimportant or inapplicable, are yet to a 
great extent capable of being employed in one and the 
same investigation. Our theories require to be grounded 
on facts, and also to be confronted with them: but to 
see our facts in the light of theory, though a dangerous 
habit, is in some ways a useful one. No practical mind 
can desire wholly to dispense with the formulated results 
of all past observation. Nor, perhaps, could such a 
desire be really satisfied : it is difficult to find a single 
case of observation that is quite free from the influence 
of our general knowledge. Whatever may be true of 
the earliest concrete assertions, at the present time 
every concrete assertion put 'forward as a thesis carries 
with it a remote and indirect reference to numerous 
' laws ' assumed. By implication it declares the posses- 
sion not only of some one piece of abstract knowledge 
but of many; it professes the knowledge not only of 
a law but of conflicting tendencies, by means of which 
the special circumstances can be allowed for and a total 
balance struck. Thus the concrete proposition (when 
so far developed as to become a thesis for proof) is 



Chap. HI.] MAIN KINDS OF THESIS. 77 

always full of abstract propositions unexpressed. Some- 
what as the trained ear can detect the overtones in a 
musical sound, the logical mind detects the hidden as- 
sumptions in a concrete proposition. The abstract pro- 
position also certainly professes an acquaintance with 
concrete facts, but not quite in the same manner as the 
concrete proposition professes a knowledge of the laws of 
Nature as bearing on the special circumstances of the 
case under consideration; for since the abstract propo- 
sition expressly avoids saying anything about special 
circumstances, the assertion made is almost infinitely 
simpler. Practically, of course, the ' overtones ' in a con- 
crete proposition are mostly overlooked, but it is their 
existence that constitutes the chief weakness of un- 
aided common-sense. What seems to common sense 
more indisputable than that this given action is a case 
of ' firmness ' or ( strength of character,' or ' courage ? ' 
Perhaps a deeper insight would show that among the 
special circumstances must be included ignorance of con- 
flicting claims, or ignorance of danger. 

There still remains to be noticed that very common 
form of proposition which, when two concrete things 
are already given as having occurred or as existing 
successively or simultaneously, asserts causal connexion 
between them. When we say, for instance, 'Your 
hasty speech was the cause of all the disturbance/ or, 
'It is this pillar that supports the building,' is the 
assertion properly abstract, as implying some law, or 
concrete, inasmuch as it speaks directly and expressly 



78 FALLACIES. [Part I. 

of individual facts ? Such propositions, I hold, may be 
used for either purpose, or for both together. It is diffi- 
cult to say for which they are most often applied, or 
even which is most often their primary meaning. On 
the whole one would perhaps be inclined to call their 
concrete meaning primary, and to say that the abstract 
meaning was rather insinuated, or implied, than directly 
intended as an assertion. But in practice it will be 
found that these assertions are largely used for appa- 
rently confirming, by means of facts experienced, causal 
laws already more than half believed. And since the 
abstract meaning has a wider importance, and since 
moreover if the assertions be true in the concrete there 
must also be some true abstract assertion behind them, 
it seems best to view them as capable of both a concrete 
and an abstract meaning, the disproval of either of which 
would disprove both. For convenience, then, we may 
speak of these as Abstract-Concrete propositions, if it be 
clearly understood that they form no new distinction in 
kinds of meaning, nor interfere with the division already 
made (of meanings, not of forms of words) into abstract 
and concrete. 

At the end of the book (Appendix E) will be found 
a table (I.) of the divisions thus far made. 

IV. Succession and Co-existence. 

There are not many minor distinctions of meaning 
in propositions that call for notice here. We are not in 



Chap. III.] MAIN KINDS OF THESIS. 79 

search of all the varieties that can possibly be distin- 
guished, nor even of such as may be on the whole the 
most important for general purposes, but only of such as 
have special interest for the purpose of discussing the 
methods and the dangers of Proof. 

It seems necessary, however, to mention briefly the 
distinction between propositions asserting succession 
(whether backwards or forwards in time) and those 
asserting co-existence ; or, as they are more commonly 
called, assertions regarding Causation, or Causal sequence, 
and assertions which merely name, or classify, the S, or 
which state some of its constant concomitants without 
necessarily attempting to trace them to a parent cause. 
Such importance as the distinction has, for us, flows 
from the fact that according to the nature of the asser- 
tion in this respect is to some extent its liability to 
special dangers. 

Wherever indication is asserted, whether in abstract 
or in concrete propositions, all importance turns, of course, 
on the degree of trustworthiness of the sign : * some 
signs being more certain than others, but even a vague 
symptom being better than none at all. And according 
as the assertion points backwards or forwards in time 
(S a sequent of £&, as in 'Valleys — > prior denudation;' 
or S an antecedent of §?, as in ' Deficient education — > 
future increase of crime ') is it to some extent open to 

* We must here use ' sign ' in an extended meaning also, to corre- 
spond to ' indication : ' so as to say that in every proposition, abstract 
or concrete, S is the ' sign,' and <§ the thing signified, or ' signification.' 



80 FALLACIES. [Paet I. 

special and different dangers : propositions pointing 
backwards being liable to the danger of overlooking 
'Plurality* of Causes;' and propositions pointing for- 
wards, to that of overlooking the liability of one cause 
to be counteracted by another. 

Thus, to take first Abstract assertions : it is seldom 
we can say that any given S invariably indicates the 
past existence of any given £&, — unless, indeed, the Jfe 
employed be so vaguely defined as to be of very little 
practical service. Every event (S) we may no doubt 
assert, within the widest empirical limits, indicates the 
past occurrence of some other event, the essential part of 
which recurring, S will recur : true, but we do not often 
find this doubted. The point of practical importance is, 
what prior events does S indicate. Or, again, every 
existing human being has certainly had (i.e. indicates 
the prior existence of) a human grandfather: this also 
is too axiomatic to convey practical information, though 
we may want to know the name or the special character- 
istics of the grandfather in question. Almost, but not 
quite, equally rare is it to find complete invariability of 
sequence asserted, except thus vaguely, when the refer- 

* Mr. Carveth Read's term, * Vicariousness ' of Causes, though less 
ambiguous, I only do not use because the name ' Plurality ' appears to 
be so firmly established, and need not really mislead. The reader to 
whom the phrase is unfamiliar must notice that what is meant is the 
possibility of any one of several causes having produced the ' same ' 
effect, as where ' one kind ' of death may be due to heart-disease, or to 
a fever, or to yet other alternatives ; the name has nothing to do with 
the combination of causes, as where a death is dne to mental anxiety, 
plus insufficient food, plus an illness not otherwise necessarily fatal. 



Chap. EL] MAIN KINDS OF THESIS. 81 

ence is forward in time. A shot through the heart or 
brain is perhaps invariably followed by death, and if 
there were interval enough between the two events we 
should say the former indicates the latter as sure to 
happen: but favourable seed-time does not necessarily 
indicate abundant harvest, since in the interval some 
unforeseen counteraction may arise, or at the seed-time 
itself along with certain favourable conditions there 
may have been an unsuspected enemy sowing tares. So 
again, we may often predict too vaguely to be of much real 
service. Sunshine, we know, for instance, always follows 
rain, and may be expected sooner or later ; but what we 
most want to know is ivhen to hope for it, or under what 
exact conditions, if within our power to compass. 

Accordingly, abstract assertions of succession are 
commonly made with a large margin for the incalculable. 
We feel fairly contented in obtaining any hint of ' law ' 
— any knowledge, that is, which may form a basis for 
even imperfectly secure inference and proof. The only 
alternative to 'Chance'* is often 'Tendency,' and in 
our gladness to escape from Chance we dignify this as 
'Law.' An abstract assertion pointing backwards has, 
then, to deduct from the trustworthiness of its asserted 
indication in order to allow for the possibility of ■ other 
causes producing the same effect ; ' and this even where 

* By 'chance' is meant in this connexion no more than the con- 
tradictory opposite of 'known law. 5 Some law there is nowadays 
always assumed to be, but that the conjunction is due to chance means 
really that no amount of limitation of S or of & will give us a known 
law between the two things so designated. See also Appendix D. 



82 FALLACIES. [Part I. 

we possess a real ' Causal Law/ It is a real law, for 
example, that prolonged starvation invariably causes 
death, But still we are very far from "being able to say 
that death, wherever found, indicates prolonged starva- 
tion. And in like manner every abstract assertion 
pointing forwards in time has, almost in proportion to 
its definiteness and consequent practical value, to allow 
for possible antidotes or counteraction. 

In abstract assertions of co-existence, we can often 
attain greater certainty of indication (for practical pur- 
poses, at least, and within narrow fields), but even here 
large use is made gratefully of incomplete laws — indica- 
tions only roughly trustworthy, true only on unexpressed 
conditions. We may know, for instance, that boys ' as 
a rule,' delight in mischief, and we may make real use 
of the knowledge, without being at all able to gene- 
ralise the exceptions so as to state a quite invariable 
law. If we could truly say, e.g. 'All boys except those 
who are physically deformed are mischievous,' our indi- 
cation would be of far greater value than while we can 
only say 'the majority,' or 'many,' or 'the average boy,' 
or any other vague limitation. 

In the concrete proposition, on the other hand (except, 
as will be presently seen, in the case where S is said to 
deserve the name §b), there can be no talk of the asser- 
tion being roughly true. The given S was either as a 
fact preceded by j£> or not ; g-> either will or will not be 
among its consequents in time. Here, accordingly, it 
becomes still more important to recognise the Plurality 



Chap. HI.] MAIN KINDS OF THESIS. 83 

of Causes and their liability to counteraction ; and hence 
the purpose of distinguishing the two kinds of assertion, 
namely those with a backward and those with a forward 
reference, — assertions explanatory or detective, and those 
which predict. As regards the descriptive or classifying 
proposition (where S is said to deserve the name gj) 
here a little more latitude seems inevitable. Names are 
altogether so loosely applied — their correct meaning 
varies habitually within such wide limits, — that in 
giving S a name not already assumed to belong to it of 
right, we may well be content, in many cases, to come 
somewhere near the mark. Is this man civilized, intel- 
ligent, learned, unsteady, idle, brave ? Even when we 
judge his character accurately in fact, very many of such 
questions might admit of the double answer, Yes and No.* 

As, then, in the case of explanatory or detective pro- 
positions the main difficulty flows from the Plurality of 
Causes, and in predictive propositions from the liability 
of one cause to be ' counteracted ' by others ; so in pro- 
positions of co-existence the danger is that of taking for 
'essential' something that is 'accidental' merely, — i.e. 
of believing 'always' when the real truth is 'some- 
times.' For if the proposition be concrete (as, 'This 
man is a fool ') it still professes abstract knowledge, — 
knowledge of the essential qualities which go to form 
the meaning of the predicate in question. 

Tables II. and III., in Appendix E, show concisely 
the results of this section. 

* See also pp. 124, 133, 184, 189, inf. 



CHAPTER IV. 

THE LAW OF COUNTER-INDICATION. 

As the presence of one thing may indicate the presence 
of another, so may presence indicate absence, or absence 
indicate presence, or absence indicate absence. All these 
are, of course, equally assertions of indication. Thus 
a negro's coloured skin may be asserted to indicate the 
presence of a cheerful temperament, or the absence of 
some other qualities ; and the absence of pain, in certain 
cases, to indicate the presence of paralysis, or the absence 
of inflammation. 

On any view of Logic, the real pon s asinorum is 
the group of facts here to be generalised under the one 
'Law of Counter-indication.'* This law may be said 
to lie directly at the root of the ordinary doctrines of 
conversion and contraposition, and also to contain an 
explanation of the whole syllogistic process. Difficult 

* Mr. MacColl, who formulates essentially the same law, adopts for 
it the name contraposition. But contraposition, in its usual meaning, 
seems never to have had quite so wide an application, and therefore I 
prefer 'counter-indication' as less likely to mislead. Cf. also Prof. 
Croom Eobertson's remarks, in Mind, No. i. p. 148. 



Chap. IY.] THE LAW OF COUXTEE-IXDICATIOX. 85 

though it is to state the law in perspicuous language, and 
intricate though some of its consequences may be, the 
principle itself is really extremely simple, and, once 
grasped, can hardly be forgotten afterwards. It needs, 
however, some special definition in order to overcome in 
the first place the difficulties of statement. 

The words ' presence ' and ' absence ' are until further 
explained, hardly general enough to express all that is 
intended, and are only chosen because no other, more 
comprehensive, names appear to be available. The pre- 
sence or the existence of a thing or quality, the happen- 
ing of an event, the truth of an assertion, stand on one 
side of the opposition intended, as contrasted with the 
absence or the non-existence of a thing or quality, the 
non-happening of an event, the untruth of an assertion. 
And for brevity and our own convenience merely, I 
wish to extend the use of the two terms chosen, in 
order to cover these diverse meanings. Accordingly 
such assertions as that ■ human beincrs — > human 
parents,' or that ' the existence of discontent in India 
— > bad government/ or that 'the falling of a stone 
— > the force of gravity, 5 or, 'If he is well he will 
certainly go; etc., are all cases of ' presence ' indicating 
'presence' in the sense intended. And so with the 
indication of absence by presence, and of presence or 
absence by absence. The two words are not to be under- 
stood as strictly limited to their ordinary sense, but as 
stretched to include the wider meaning postulated as 
above for the sake of simplifying the expression. 



86 FALLACIES. [Part I. 

Now, since we mean by S the whole of that ' thing ' 
which constitutes the sign or datum, and by jo the whole 
of that which the sign signifies, it is clear that if we 
employ symbols to express respectively that thing the 
presence or absence of which may indicate jo, and that 
thing the presence or absence of which may be indicated 
by S, we cannot use S and j& themselves for such a 
purpose without incurring misinterpretations. Instead 
of them it would be better, where necessary, to use the 
corresponding small letters s and S. Thus, if the presence 
of a steady pulse — > absence of fever, ' steady pulse ' 
and ' fever ' are respectively s and g, ' the presence of a 
steady pulse ' is S, and ' the absence of fever ' is j&. 
Finally, if we call that S or J which expresses the 
'presence' of s or S, a positive one; and that which 
expresses their ' absence ' a negative one ; and if we call 
their positiveness or negativeness their quality ; and the 
change from positive to negative, or from negative to 
positive, a change of quality ; the law may be stated as 
follows : — 

All indication of jo by S {affirmed or denied) is ex- 
pressible as indication of S by jo (affirmed or denied), 
if, and only if, the quality of both S and jfc be changed. 

Let us trace the operation of this law, first symboli- 
cally and afterwards by means of examples. And for 
the symbolical expression let S and j& stand for the 
positive forms, and non-S and non-j^ for the negative 
ones. Then the sole equivalent of 



Chap. IV.] THE LAW OF COUNTER-INDICATION. 



87 



(1) 


s-> & 


is 


non- J^ — ^ non-S 


(c/. contraposition of A) .* 


(2) 


S — >- non-Jj) 


» 


J^— ^ non-S 


(c/. simple conversion of E).* 


(3) 


non-S — > §$ 


» 


non- JJ> — > S 


(cf. exclusive disjunction).* 


(4) 


non-S — ^ non-J}> 


jj 


£-» s 


{cf. No. 1, above). 



and the sole equivalent of 



(5) 


S+> £ 


is 


non-J£>-|-> non-S 


(c/. contraposition of 0).* 


(6) 


S -B* non-<g> 


j) 


£+> non-S 


(c/. simple conversion of I).* 


(7) 


non-S +> g 


>> 


non-^-f^ S 


(cf. No. 3, above). 


(8) 


non-S +-> non-J£> 


>> 


S>+> s 


(cf. No. 5, above). 



But examples will perhaps show the process more 
clearly. Take first the assertion that "every corrupt 
tree bringeth forth evil fruit" (i.e. presence of corruption 
in the tree — > ditto in the fruit) ; then the equivalent 
form of this, and the sole indication implied, would be 
1 absence of corruption in the fruit — > absence of cor- 
ruption in the tree ' (i.e. * if the fruit is sound, the tree 
is sound '). What the proposition does mot tell us, but 
what may perhaps be known to be true from other 
sources, is, either that corruption in the fruit indicates 
corruption in the tree (i.e. " every tree that bringeth 
forth evil fruit is corrupt"), — which would be the 
' simple converse ' of the original proposition, — or that 

* These names refer to some of the ordinary technicalities of Logic. 
They are well explained in all the text-books ; e.g. Bain's Deduction, pp. 
113-116, 122. 



88 FALLACIES. [Part I. 

soundness in the tree indicates soundness in the fruit — 
which would be the 'reciprocal.' From the original 
proposition, we can indeed get the denial of any such 
law, as that corruption in the fruit indicates soundness 
in the tree {i.e. ' Some corrupt fruit is the offspring of a 
corrupt tree ; ' the ' converse per accidens ') ; but this, 
being a denial, is not itself a statement of indication : the 
sole indication is that which in the A and propositions 
is usually called the ' contrapositive,' in the I and E 
propositions the ' simple converse,' and which in all 
propositions is here called the counter-equivalent. 

Or take (2) the assertion that 'no quakers are dis- 
honest ' (quaker tenets — > absence of dishonesty.) Of 
this the formal equivalent would be that dishonesty — > 
absence of quaker tenets (' No thieves are quakers '). 
Here will at once be recognised the ordinary simple con- 
verse of E, our rule differing, in fact, from such conver- 
sion only in being applicable more generally, so as to 
include all grammatical forms of proposition, so long as 
they express the indication of non-S>. Thus from the 
conditional sentence, 'If it be true that he has come, 
then it must be false that he has broken his leg;' we 
get by counter-indication, 'If it be true that he has 
broken his leg, then it must be false that he has arrived.' 
Again, from (3) " He that is not with us is against us " 
(or 'Everyone is either with us or against us,' or 'All 
except our party are unfriendly') we get by counter- 
indication some proposition meaning that all except the 
plainly hostile are on our side; and if the proposition 



Chap. IV.] THE LAW OF COUNTER-INDICATION. 89 

should prove untrue in one of its aspects it must be 
untrue in the other also. This form of proposition de- 
serves more attention in Logic than it sometimes obtains, 
and we shall presently (p. 92) have to devote a few 
words of special notice to it. It is perhaps more liable 
to misinterpretation in respect of its legitimate counter, 
than any of the other forms.* 

The importance of the Law of Counter-indication is 
far-reaching in Logic. But so far as relates to the in- 
terpretation merely of the meaning of assertions it may 
be shortly stated. A certain proportion of indications 
there are — a comparatively small proportion, however — 
which really ' cut both ways,' or, as it is technically 
called, allow of the ' reciprocal ' f assertion also. Thus, 

* As examples of the remaining forms may be given : from (4) ' with- 
out trouble there can be no success/ ' the attainment of success shows 
that trouble has been taken : ' from (5) ' typhoid fever does not neces- 
sarily show that there has been defective drainage,' ' proper drainage is 
no complete safeguard against typhoid fever : ' from (6) " the presence 
of the attribute 'habitual tendency to drunkenness' does not neces- 
sarily show the absence of (or ' is compatible with ') a fair amount of 
industry " ' the presence of a fair amount of industry does not neces- 
sarily show the absence of a tendency to drunkenness ' (or, from ' some 
habitual drunkards are fairly industrious ' ' some fairly industrious men 
are habitual drunkards'): from (7) 'absence of the power of discrimi- 
nation does not necessarily mean presence of the power to generalise,' 
' absence of the power to generalise does not necessarily indicate pre- 
sence of the power to discriminate : ' from (8) ' illness does not necessarily 
mean weakness,' ' strength does not necessarily mean health.' 

t The name ' reciprocal ' will be here slightly extended beyond the 
ordinary usage, and employed to mean not only what Prof. Bain calls 
(Logic, vol. i. p. Ill) the " material obverse," but also the illegitimate 
converse of any indication (affirmed or denied) ; i.e. the converse formed 
without changing the quabty of S and <£. Thus, both 'non-S — > non.£? ' 



90 FALLACIES. [Part L 

evil fruit does perhaps, as a fact, indicate an evil tree. 
So again, while a certain label on a bottle shows that it 
came from a certain firm (S indicates 3b), we are also 
often told, in the same breath, that " without such label, 
none are genuine " (non-S indicates non-§->) ; and while 
equilateral triangles are equiangular, equiangular triangles 
are equilateral. From these and similar occasional cases 
a certain looseness has affected our application of all 
words expressing indication (the word ' indication ' itself 
seems to me least ambiguous of any) through which its 
essential one-sidedness comes into frequent danger of 
being forgotten. The law of counter-indication helps 
to remind us that sign and signification are not quite 
identical. 

Here should be noticed further a fact which interferes 
largely with what may be called the positive utility of 
the law, — the fact, namely, that s is so often a mark 
whose presence or absence is much easier to recognise 
than that of S. When Darwin finds, for example, that 
white cats, with blue eyes, are always deaf, the counter 
equivalent (absence of deafness, in cats, — > non- white- 
ness of fur or non-blueness of eyes) is hardly likely ever 
to be used as a direct indication. If we want to discover 
the colour of a given cat's eyes, we should probably use 
our own, by way of direct observation, rather than 
employ a series of experiments upon the cat's power of 

and ' & — > S ' would be forms of the ' reciprocal' of ' S -> £.' See 
also Wundt's remarks on 'one-sided' and 'mutual' dependence in 
general; Logik (Erkenntnisslehre) , pp. 214, 245, 317, etc. 



Chap. IV.] THE LAW OF COUNTER-INDICATION. 91 

hearing. And so in many other cases. The chief value 
of the law is rather restrictive than inferential, — namely 
to prevent our supposing the reciprocal necessarily true. 

Readiness to accept the reciprocal as equivalent, is 
one of the strongest tendencies in uninstructed human 
nature. Recognising, for instance, the rough truth of the 
law that stupid people are conservative, the superficial 
reasoner is apt to overlook the difference between this 
assertion, and that ' to be conservative — > stupidity ; ' 
assuming that success in examinations is a good indi- 
cation of hard work and high talents, common sense 
supposes that this assertion really means that failure in 
examinations is a good indication of idleness or incom- 
petence ; only with great difficulty can the illogical 
mind be made to see that other causes of such failure 
can possibly exist besides the one or two most superficial 
or striking ; and when the plurality of causes is at last 
recognised here, it seems to shake some people's faith in 
the positive indication also. Professor Jevons, speaking 
with a wide knowledge of students' capabilities, tells 
precisely the same tale. "A man," he says, "who is 
very ready at integration begins to hesitate and flounder 
when he is asked such a simple question as the follow- 
ing: 'If all triangles are plane figures, what informa- 
tion, if any, does this proposition give us concerning 
things which are not triangles ? ! " To some extent also, 
and chiefly where symbols are employed, no doubt 
the error flows from a mere thoughtless inclination for 
balance, or antithesis, or symmetry. Those who are just 



92 FALLACIES. [Part I. 

beginning the study of Logic are perhaps especially- 
apt to be slaves to this inclination. De Morgan notices 
(and Jevons endorses the opinion) that the average 
beginner, when asked what follows from 'Every A is 
B,' invariably and promptly answers, 'Every B is A 
of course.' One cannot help feeling that the cause is in 
such cases probably not very deep ; the schoolboy who, 
being told that the three sides of a certain triangle were 
equal, triumphantly inferred that the fourth side must be 
equal too, hardly supplies a better instance of simple 
want of thought. 

Most of all, perhaps, in interpreting the thoroughly 
'disjunctive' proposition (where absence is asserted to 
indicate presence), this spirit of superficiality may be 
seen in harmful operation. That is to say, a disjunction 
is relied upon as exhaustive while it is thought sufficient 
to prove the mere assertion of difference. Thus 'Con- 
servative' and 'Liberal' are certainly different, but it 
does not follow that they are the only two alternatives. 
The counter-equivalent of ' non-S — > £o ' is, as shown 
above, 'non-§-> — > S,' but what is thus wrongly taken 
as equivalent is ' £$ — > non-S,' — a proposition almost 
always far easier to prove. 

For when we say that " If not s, then % ' we make a 
large assertion. We divide, in fact, the whole universe into 
two classes, s and S, and boldly assert that nothing else 
but these exists,— that whatever is not in the one class 
must be in the other. Now, to do this with s and not-s. 
or with % and not-S, is a matter of common occurrence ; 



Chap. IV.] THE LAW OF COUNTEK-INDICATION. 93 

so common, in fact, that whenever we use a general name 
we tacitly accept thus much responsibility. But in such 
cases the only difficulty is as to the position of the 
dividing line, not as to the outer limits of the field that 
may lie beyond it : f not-s/ or ' not-S ' does not bind us 
to specify otherwise than quite vaguely the things that 
lie outside our defining fortification. 

"When, however, we go further and say, 'I know a 
positive name for the whole class, not-s (e.g. ' not-con- 
servative '), and that name is %,' (e.g. ' liberal ') we really 
profess to have looked out from the citadel s, and to 
have scanned the universe therefrom. Of course there 
are cases where, owing to special circumstances (e.g. 
artificial limitation of the ' universe,' * or again, the case 
where s occupies a larger extent than not-s) this is prac- 
tically possible. It needs little courage to assert that all 
the contents of my pocket are either letters or post- 
cards, or that if a man does not believe the earth is 
round, he must be slightly crazy. But there are many 
more cases where we are apt mistakenly to suppose the 
universe scanned ; and this danger is immensely increased 
if we are careless enough to suppose that it is ' the same 
thing* (or even 'practically' the same thing) to prove 
the reciprocal. 

* De Morgan was, I believe, the first to observe that behind most 
assertions there is an unexpressed limitation of the range of their extent. 
There is a ' universe of Discourse ' beyond which the assertion is not 
intended to apply. ' Not-white/ for example, is predicable solely within 
the universe • colour ; ' and ■ Nonconformist ' excludes, by custom, 
heathens and atheists, as well as those who conform. 



94 FALLACIES. [Part I. 

But mere thoughtlessness is, no doubt, not the only 
explanation of the tendency in question. The deepest 
source of it seems to be the fact that provisional belief in 
the reciprocity of indications is so often fruitful as 
regards the earliest guesses at unknown truth; for 
though £& (or non-S) may not exactly indicate S (or 
non-§i>), it is often so closely connected with it by causa- 
tion that in finding where such indication fails we hit 
upon the real law. Corruption in the fruit, for example, 
may except in certain assignable cases indicate corruption 
in the tree. Nevertheless, in Proof as distinct from 
Discovery, the tendency is fatal, and needs to be held 
in severest check. It is unsafe even to suppose, as 
seems so natural, that mutual indication is the rule, and 
one-sided indication the exception. Probably the pre- 
vailing attitude among the illogical is best expressed as 
the belief that any law, in the absence of proof to the 
contrary, involves a 'fair presumption,' at least, that the 
reciprocal is true; while fair presumption is not worth 
distinguishing from ' practical certainty : ' the real fact 
being that the most an abstract indication ever involves 
is a fair presumption (and that not always) that the re- 
ciprocal is worth the labour of investigation. But it 
seems unnecessary to say more about the practical value 
of the law of counter-indication : it merely binds up into 
one scheme rules whose utility is already well-known. 
This is the case, at least, as regards the universal affirma- 
tive and the particular negative : perhaps, however, the 
ease with which the disjunctive proposition is liable to 



Chap. IV.] THE LAW OF COUNTER-INDICATION. 95 

be taken for the mere assertion of difference, may be a 
less familiar fact. 

It remains to ask how far the law is applicable to 
concrete propositions The answer seems to be that, 
though formally implied, the counter-equivalent is in 
concrete propositions never directly needed. This is in 
fact the extreme case of what was noticed in the example 
of the blue-eyed cats. Jf s be a concrete ' thing/ we have 
other marks, more readily applicable than non-§j, by 
which to prove its absence : it is in fact known to us 
mainly by means of its attendant circumstances as a 
whole ; and % is only one of these, and (by hypothesis) 
not the most familiar. We can, indeed, apply counter- 
indication to concrete matter in some such way as this : 
suppose the concrete proposition to be ' This murder 
— > greed of gold ; ' if we are certain of this, and also of 
the fact that in a given prisoner's case the greed of gold 
was absent (non-Jfe), we no doubt may infer that this 
murder was not (non-S) committed by him. But here, 
of course, it is not ' this murder ' whose existence we 
get denied, but the truth of the theory that it indicates 
the prisoner as its cause : it seems that the result is 
obtained circuitously, by means of the abstract indi- 
cation involved, — namely ' Any one who committed this 
murder must have had a greed of gold/ or ' The abstract 
possibility of this murder — > such motive/ and this 
motive was absent in the case before us : hence, in 
the case before us ' this murder ' was absent too. This is 
better viewed as a case of highly elliptical syllogism than 
of Immediate Inference. 



96 FALLACIES. [Part L 

There is one further precaution to be observed in 
using the law ; a precaution, however, which is probably 
too simple to require notice except so far as symbols are 
employed. And perhaps the reader already recognises * 
that half the mental confusion that exists is really due to 
the use of symbols, — whether such symbols are imposed 
upon us by the real need for abbreviation (as e.g. in the 
case of general names), or by what may appear to be 
the wanton pedantry of logicians. It is easy enough, for 
instance, to see that the proposition 'Every man is an 
animal ' does not imply that every animal is a man, 
though possibly some people might be less clear about 
it if A and B were substituted for Man and Animal. 
Latet dolus in generalibus. But here the source of con- 
fusion to which I wish to draw attention is that due to 
the time-element in indications. Where propositions of 
co-existence are in question, no difficulty can possibly 
arise, but in the case of succession it may be worth while 
to notice that where S indicates (or fails to indicate) 
future §b, non-£b indicates (or fails to indicate) past non- 
§b, and where S indicates (or fails to indicate) past §b, 
non-£o indicates (or fails to indicate) future non-£&. The 
examples, given above, of the connexion between labour 
and success, or between typhoid fever and the drainage,! 
were chosen with the view of showing this necessity. 
Practically, where actual examples are employed the 
danger is not likely to arise ; but in the absence of an 

* With Mr. Keynes, Mind, No. xv. p. 366. 
t See note on p. 89 : examples (4) and (5). 



Chap. IV.] THE LAW OF COUNTER-INDICATION. 97 

express caution there might perhaps be a tendency to 
suppose that f S — > future S> ' is equivalent to ' non-gj 
— > future non-S,' with which indication (as would be 
seen at once when translated into full language) it has 
really nothing to do. 

Less important does it seem to mention that mere 
puns form no exception to the law. No reader, I hope, 
will be puzzled by the fact, for example, that while the 
presence of courage clearly indicates ' presence of mind/ 
it by no means follows that ' absence of mind ' indicates 
anything approaching to cowardice. Logic presents ad- 
mirable opportunities for those who find amusement in 
punning, — a fact largely recognised some two thousand 
years ago. But at present we are not concerned with 
any difficulties due to merely verbal quibbles. 

There remains little more to be said here about the 
subject-matter of Proof, except to admit as unmistakably 
as possible that the view of propositions here taken, and 
the classification here made, is far simpler than would 
be required for almost any purpose other than ours. For 
Psychology certainly, and also for the doctrine of In- 
ference in general (as contrasted with reflective Inference, 
or Proof) very much more would be needed. But in 
Proof we start always with some completed Judgment, 
some Judgment developed so far as to be expressed, 
reflected upon, and its validity called in question : hence 
the growth or formation of the Judgment from its earliest 
traceable stages is of no direct concern to us. Many of 
the varieties of grammatical structure correspond roughly 



98 FALLACIES. [Paet I. 

to shades of meaning which vary both in definiteness and 
strength of assertion, and in richness of implication. 
These are in themselves of high importance : but before 
the interest in these arises we need to keep perfectly 
clear the first broad distinction between proven and not- 
proven. For such a purpose the plan which commends 
itself alike to common sense and to Logic, is that of 
treating the proposition as something put before us in 
an already formed condition; put forward, that is, as 
conveying intelligible meaning and deserving intelligent 
belief. By considering it a pretender to these qualities, 
and then proceeding to inquire how far it actually falls 
short of attaining them, we best arrive at some notion 
of its real position on the long scale between worth and 
worthlessness. It is on this account that we choose, as 
being of directest interest, the task of considering in 
detail the series of possible objections that can be brought 
against any thesis set up as worthy of belief. 



CHAPTER V. 

THE PROCESS OF PROOF, IN GENERAL. 

I. The Relation between Thesis and Reason. 

What is the relation between a thesis, as such, and any 
reason given for it ? What is really said in saying, • the 
proposition T * is true, because the proposition R * is 
true ' ? This question lies at the root of the doctrine of 
logical sequence. 

To prove an assertion, it was said in Chap. L, is to 
establish it in full view of hostile criticism : the function 
of the advocate being to find and bring forward reasons 
for belief or disbelief, and the function of the judge 
being to weigh the evidence brought forward, balancing 
the arguments for and against. Our concern, it has 
been also explained, is entirely with the latter of these 
functions, and accordingly we may dispense with all con- 
sideration of the finding of the arguments. 

But suppose an argument already found and pro- 
duced — suppose, that is, not only a thesis brought for- 

* For convenience, T and R will, throughout, be occasionally used 
for 'Thesis' and 'Reason' respectively. 



100 FALLACIES. [Part I. 

ward, but also a reason or reasons in support of it ; * by 
what means are we to judge of the binding force of such 
argument, how test the validity of the reasons given, or 
the strength of the evidence adduced? The answer to 
so large a question cannot be given briefly and directly, 
except in words too general to render real assistance in 
the special cases. But it may be worth while first to 
take the broad and distant view. Clearly the most 
preliminary requisite is that no mistake should be possible 
as to the full relation between Reason and Thesis, as 
proposition guaranteeing and proposition guaranteed. 

We elected also (p. 73) to neglect the distinction be- 
tween categorical and hypothetical propositions, as stand- 
ing outside our interest ; and to treat all propositions, 
whatever their grammatical form, as alike in stating a 
relation between two terms. But in order to do this it 
was necessary to explain that the terms of a proposition, 
so understood, are sometimes themselves propositions, — 
as in the familiar case of the ordinary hypothetical. Now 
every argument may be viewed as a proposition of this 
character, with subordinate prooositions as its terms. 
Every argument states that the truth of R indicates the 
truth of T. Every argument, that is (to apply the law 
of counter-indication), whatever else it says, makes an 
assertion expressible in the formula : — 

K -> T, and 

non-T — ^ non-B. : i 

* Seasons for any thesis are, of course, reasons against the opposite 
one ; and the expression may therefore be safely generalised as in the 
text. 



Chap. V.] THE PEOCESS OF PEOOF, IN GENEEAL. 101 

which is the symbolic expression for 

" Grant E, and T follows, and 
Deny T and the denial of E follows." 

Or, since in every argument the truth of the Reason is 
asserted to guarantee that of the Thesis, every argument 
also asserts that unless the Thesis were true, the Reason 
would be false. 

But this is not all that an argument, as such, asserts. 
There is another element in every case of attempted 
proof; * namely, the assertion of the material truth of 
the Reason. Without this, the relation asserted would of 
course fail in relevance to the matter in hand. Unless 
the reason brought forward for believing a thesis be itself 
asserted to be true in fact, the argument as a whole would 
clearly be devoid of all meaning. It is no argument to 
say that if some false or doubtful proposition were true, 
the thesis would be true: to support (e.g.) the thesis 
" England is on the verge of ruin " by declaring " I could 
appeal to statistics if only they were different," or even 
by means of the reason "Because possibly statistics 
would show." -f* In other words, failure in material truth 

* Cf. Mr. H. MacColl. Mind, xvii. 55. " The statement * a, there- 
fore 6 ' is stronger than the conditional statement ' a implies &,' and 
implies the latter. The former asserts that b is true because a is true ; 
the latter asserts that b is true provided a be true." 

f The mere mention of so trivial a fact as this second element 
in the full meaning of an argument, seems to need some apology ; 
and the present is a good opportunity for remarking that wherever self, 
evident truths are enunciated in discussing the underlying principles of 
Logic, the purpose is by no means to convey new information, but rather 
to go through the duty — irksome alike to reader and writer — of formally 
6 



102 FALLACIES. [Part I. 

of the Reason is one danger which every argument must 
avoid ; the sole other danger being that of failure in the 
formal adequacy of such Reason, — i.e. the material un- 
truth of the asserted relation between R and T. Any 
argument, in short, is liable to frustration in two 
ways : — 

(1.) If R be in fact untrue : 

(as, perhaps, where England's impending bank- 
ruptcy is appealed to in proof of the disastrous 
effects of Free Trade.) 

(2.) If R can be true while T is false : 

(as where the Sun's movement round the earth 
was the Thesis, and the facts of 'rising' and 
' setting ' were the Reason given.) 

As to the first of these two possible attacks on Proof, it 
is clear that when once the question is raised whether R 
be true or not, R becomes itself a new Thesis, and must 
either be accepted without further inquiry or submit in 
turn to have its own grounds produced for examination ; 
the same difficulty recurring until a basis of accepted 
truth is reached. It is therefore sufficient for Logic, as 
such, to carry the analysis of the methods of Proof up to 
the point where the formal adequacy of the reason given 
is secured, thus guarding against the second of the two 
attacks : for the first of them leads to a mere repetition 
of these methods, only on new subject-matter. Can then 

registering such facts, merely to prevent possible misunderstandings, and 
for convenience in afterwards referring to them. 



Chap. V.] THE PROCESS OP PROOF, IN GENERAL. 103 

the highly generalised statement, given above, of the 
nature and needs of formal adequacy be translated into a 
shape somewhat more convenient for application to actual 
arguments ? This question will need a rather circuitous 
answer. 

II. Consistency. 

Probably there is no meaning more universally asso- 
ciated with the epithet ' logical ' than that of pushing to 
the extreme. That is to say, a man is popularly said to be 
logical (whether as a term of admiration or of the reverse) 
in proportion as he shows a tendency to push accepted 
principles to their legitimate outcome. The logical 
person is, as a rule, uneasy under any system which, 
while refusing expressly to modify inconsistent principles, 
tosses them together and take3 the mean result. In his 
simplicity he supposes that whatever is asserted as true 
must be intended as strictly true, — true even in its 
extreme case : a principle false in a single instance 
becomes to him fallible altogether. Hence he is apt to 
lack that quality which may be flatteringly called the 
delicate tact and skill required for handling political or 
ethical fictions with advantage, or for utilising to the full 
certain ancient structures thickly coated over with 
anomaly. The English Constitution, English Law, the 
English Church, present to such a person continual diffi- 
culties. He demands a clear understanding or no pretence 
of it, codification or else anarchy, absolute submission to 
authority or else absolute freedom from it. In this sense 



104 FALLACIES. [Part I. 

it is that the French are called in every newspaper a 
logical nation, while the English (with the exception 
perhaps of a portion of the reforming party) have in 
many quarters quite an opposite reputation. 

But this is not all. Besides reading the remoter 
consequences of principles which are ready-made, the 
logical person is apt to generalise principles, on his own 
account, out of isolated facts. Besides being tenax 
propositi, he is eager for justice to be dealt. Not con- 
tent with demanding that an actually asserted principle 
(a ' universal ' or 'abstract ' assertion) shall be true in 
its extreme cases, he is inevitably inclined to take even 
purely concrete or individual assertions as covertly 
asserting a principle, — any disclaimers on the part of the 
assertor notwithstanding. Thus, if the ' logical ' Legis- 
lator finds some individual, or some class, in possession of 
a certain right or subject to a certain duty, he is always 
under strong inclination to extend such right or duty to 
analogous cases : if householders and lodgers in a borough 
have a vote, he is apt to view them as members of a 
wider class including (at least) householders and lodgers 
elsewhere : he resists a Permissive Bill on the ground 
that it is 'illogical' to allow the sale of liquor in one 
district while prohibiting it in another, — if alchohol is 
pernicious at all, he argues, it is pernicious everywhere ; 
or if the ratepayers are to have this prohibitory power 
they must * logically ' be allowed the like power in other 
cases, until there might be nothing left of individual 
liberty. So again, he considers it indefensible to protect 



Chap. V.] THE PKOCESS OF PROOF, IN GENERAL. 105 

one branch of industry without protecting all. In a 
word, behind apparently simple individual facts, he has 
a keen eye for possible principles involved. 

In appealing in this way to what is after all only a 
loose and popular meaning of the word, I must not be 
understood as laying more stress on such meaning than it 
deserves. Popular usage is often, of course, as misleading 
as etymology, when the purpose is to find the most 
accurate sense of a term at the present day. But as 
already explained, such purpose lies altogether outside 
our interests, our only desire at present being to gather 
in from any source available the broadest preliminary 
notions. And while the loosest custom is ever the most 
widely spread, the widest custom has the best chance of 
indicating, however vaguely, the more permanent founda- 
tions of meaning. 

The two correlative ' logical' tendencies just noticed 
have, it is true, only a remote and indirect connexion 
with the needs of formal adequacy ; but their recognition 
may serve very well to bring us a stage nearer to the 
actual point. If to be logical is, mainly, to be consistent, 
perhaps a glimpse at the nature of consistency will afford 
a closer view of the point in question. 

The Maxims * of Consistency (also often called the 
"Laws of Thought") are commonly given as three in 
number, — The Laws of (1) Identity, — A is A ; (2) Con- 
tradiction, — A is not not-A; and (3) Excluded Middle, 
— A is either B or not-B. Whenever we use a name, we 

* Bain : Logic, i. Introd. sect. 22. 



106 FALLACIES. [Pabt L 

use by implication the whole meaning belonging to that 
name, both (1) positively, and (2) negatively: and (3) 
every ' thing ' either deserves any suggested name or does 
not. By the first Law, for example, 'a man's a man/ 
whatever else he may also be. And by the second, we 
must take care that our defining-line is clearly drawn. 
What is outside A must not be confused with that 
which is within the range of its meaning. A name may 
be qualified, i.e. may have other (compatible) meanings 
added to it, as when we speak of ' a strong man, armed ; ' 
but incompatible meanings cannot * be joined to it with- 
out reducing its employment to absurdity by taking 
away the meaning already given ; so long as two contra- 
dictory meanings are supposed to remain in force, each 
neutralises the other, leaving the total name a blank. A 
straight line which is also, in the same plane, a curved 
line, is no line imaginable by us at all. 

Trivial though these twof Laws may appear when 
viewed either as Postulates of Language or as statements 
of psychological fact, yet as practical maxims for ensuring 
the consistent use of names they are evaded or violated 
by everybody every day; and though it may well be 
held that absolute obedience to them is, in the present 
state of language at least, practically impossible, it cannot 
be denied that as ideals they have a certain use. At 

* Except as hereafter explained, see p. 139. 

f The third law, (excluded middle), deducible from the other two, 
first comes into importance when we deal with the subject of misinter- 
pretation. For the present it may be left aside. fu . < 



Chap. V.] THE PROCESS OF PROOF, IN GENERAL. 107 

present, however, our sole purpose is to connect them with 
the needs of formal adequacy in general 

We seem to have made perhaps rather an abrupt leap, 
from speaking of holding to Principles, and of rational- 
ising our isolated beliefs by bringing them under Prin- 
ciples, to the question of abiding by the postulated 
meaning of names. But there is no great leap after all. 
A general name may be viewed either as something to be 
applied (and thus, in effect, a Principle) or as something 
to be defined (and thus to be brought under a wider 
Generality) * The use of a general name is twofold 
always, — to be given to a ' thing/ and to signify certain 
supposed facts about that thing. Names, in fact, so far 
as used at all, can only be used as terms in a proposition, 
whether as S or § : every general name is applicable to 
something namcable, and signifies some other nameable 
thing or things. 'Man' denotes (as Mill phrased it) the 
individual men, and connotes the attributes essential to 
the class. Accordingly the process of attempting to 
abide by the meaning of our names is, at bottom, iden- 
tical with that of attempting to abide by our assertions : 
and in speaking of one we speak of the other. 

Every name, then, that has a meaning, by virtue of 
that meaning refers the object named to its place in a 
system of wider and narrower classes : to state the full 
meaning of any name f (or as it is technically called, to 

* If N stand for ' general name,' then we may symbolise the nse of 
names as S — ^ N — ^ J5. 

f Otherwise than by merely giving a synonymous term. 



108 FALLACIES. [Part I. 

define the corresponding notion), in every case without 
exception consists in mentioning some wider class {genus) 
of which the things designated form a part, and also 
mentioning the marks {difference) by which the part in 
question may be distinguished from the whole remainder 
of the wider class. Thus • city ' might be defined as ' a 
large town {genus) possessing a cathedral' {difference). 
And if, accepting this definition, we make the assertion 
' Manchester is a city/ we state really two things about 
Manchester, — (1) that it is a large town, and (2) that it 
possesses a cathedral. 

Either of these two elements of the meaning of every 
significant {i.e. 'general') name, — the generic or the 
differential element — may from various causes become 
obscured or sink out of sight. One set of minds find 
a standing difficulty in seeing the wood for the trees, 
another set habitually fail to see the trees for the wood : 
the former, fixing their attention mainly on the points of 
difference, forget the common link that binds the members 
of a class together ; while the latter stop at the broad 
resemblance, disdaining, or dreading, or simply not per- 
ceiving, the obscurer differences of detail. The term 
1 city ' of course, being quoted here specially on account 
of its simplicity of meaning, does not well exemplify 
either difficulty : but the majority of general names do 
exemplify it, more or less. A negro, for instance, is 
'man,' with a difference, and perhaps the disputed 
question whether he is a ' man and a brother ' will supply 
an example of what is here meant — some people, through 



Chap. V.] THE PEOCESS OF PROOF, IN GENERAL. 109 

seeing clearly that he is not a ' brother/ being inclined 
to treat him as hardly human ; while others, through the 
obvious fact of his humanity, have perhaps rather over- 
looked his differential qualities. It is not always, then, 
so simple a matter as it might seem at first, to take care 
that A means really A, and not at all not-A ; and what 
is worse, owing to the unavoidable faults of language it 
is only possible within somewhat narrow limits to " call 
things by the same names as other people." But here it 
is sufficient to notice in the first place that it is the Law 
of Identity which (viewed as a practical maxim) bids us 
recognise the generic element in the meaning of a name, 
while the Law of Contradiction draws our attention to 
the differential line. 

Names, then, are employed in Proof as tickets, or 
marks, or signs. Every general name is a significant 
label, intended to make a two-sided assertion about the 
thing that bears it. And consistency demands that 
whenever we apply a name we shall be prepared to face 
all consequences and abide by the full meaning of such 
name: to fail in doing so, is to be inconsistent, and 
thereby to destroy the value of our own assertion. 

This demand, it will be seen at once, corresponds to 
the first of the two logical tendencies noted above, namely 
the holding to our Principles. A Principle, in the sense 
there used, is nothing more than a universal or abstract 
assertion. To bring any case under a law or principle 
is precisely the same operation as to bring any S within 
the range of a name : the purpose in both cases being to 



110 FALLACIES. [Part I 

make use of generalised knowledge already supposed to 
be true. On the other hand the second logical tendency 
— extension to analogous cases — is a much more com- 
plicated affair, being partly mere deductive * consistency 
and partly a process far more difficult to guard from 
error. The main feature in the second case is in fact 
not merely the application of abstract assertions, but also 
their formation, — a process which has often to be carried 
on with dangerous speed and without the aid of fully 
outspoken statement. Here too, however, exactly the 
same two fundamental dangers are present, — namely on 
the one hand that of overlooking points of difference 
(between the cases supposed to be analogous) and thus 
generalising too widely; on the other hand that of 
neglecting points of resemblance, and thereby not ex- 
tending the principle far enough. In both kinds of Con- 
sistency (accepting for the moment the popular name) all 
turns upon our accurate appreciation of the points of 
difference and resemblance : but in Deductive Consistency 
we are concerned with the differences and resemblances 
generalised and acknowledged already in the names 
employed, while in Analogical Consistency the point of 
primary importance is the nature of the things them- 

* As this is the first occasion where the name ' deductive ' has to 
be here employed, it may be well to explain, for those to whom the 
term is unfamiliar, that deduction, whether used in Inference or in 
Proof, is always the process of interpreting a law in its details, or 
applying it to the particular cases which it is intended to cover. This 
may be easily remembered by viewing the process (Deduction) as a 
downward one, — law being ' higher ' than fact. 



Chap. V.] THE PKOCESS OF PROOF, IN GENERAL. Ill 

selves, and the extent and kind of difference and re- 
semblance really existing between them. 

III. Formal Adequacy in general. 

By failure in formal adequacy of the Reason, is meant, 
it was said, every case where R can be true while T is false. 
It now becomes important to look more closely at the 
nature of R in general, inquiring what (if anything) is 
universally characteristic of such assertions as are capable 
of supporting a Thesis. 

Since by R we mean only the reason actually given 
or expressed, it must be admitted that there is no 
universal property of R, as such, except those already 
mentioned, — namely such as are involved in the mere 
relation between any Reason and any Thesis. But if 
instead of the ' Reason given ' merely, we speak of the 
whole ' rationalisation ' of the Thesis, — the reason, if 
any, implied, as well as the reason expressed — the case 
becomes very different. For two elements, express or 
implied, are required for all rationalisation: (1) a Principle 
or abstract indication (an assertion that a certain sign is 
trustworthy) ; (2) an Application of such Principle, or an 
assertion that the sign is present in the case or cases 
contemplated by the T : in other words, all rationalisa- 
tion may be represented syllogistically. 

Proof is thus, in an important sense, the counterpart 
of Explanation, The two go hand in hand, and each is 
only possible in presence of the other. Just as explan- 



112 FALLACIES. [Part I. 

ation always demands a reference to some wider Gener- 
ality than that which is to be explained, so Proof always 
demands a reference to some wider Generality than that 
which is to be proved. To explain, and to prove, consist 
essentially in this.* Both are forms of ' rationalisation.' 
It must not indeed be supposed that such ' wider gener- 
ality' is always in the first place formulated, even in 
thought, — much less in language. The kind of evidence 
called circumstantial, for instance, and still more the 
argument from analogy (or 'parallel cases') are by nature 
averse from any such restrictive procedure, preferring 
rather to keep their principles as dim and intangible as 
possible. But none the less is some principle, however 
limited (so only that it be wider than the thesis itself), 
required before any test can be applied; and the main 
business of Logic, as a practical science, is to force, in 
every case, such principle into explicitness, in order to 
see whether or no it and its application can bear the 
daylight, or stand the strain of stubborn fact. An 
argument, like a chain, must of course be tested by its 
weakest part: and while either the principle or its 
application, or both, may be unwarranted by fact, it is 
the principle itself which presents at least the largest 
target for attack, and which is therefore oftenest the 
centre of logical interest. Behind every reasoned belief 
there is at least one abstract proposition more or less 

* We have seen above (p. 108), how in the case of explaining the 
meaning of a name, the process (Definition) always refers the thing 
named to some higher genus. 



Chap. V.] THE PROCESS OF PROOF, IN GENERAL. 113 

vaguely implied : and the most potent engine of disproof, 
— and through disproof, of proof, — is the process that 
brings to light these underlying abstract propositions, in 
order that their validity may be called in question. The 
rationalisation of knowledge is its reference to principles 
sufficiently secure from criticism ; and it is the Syllogism 
which helps us to force these principles into explicitness 
in any given case, and so enables us to inquire into the 
foundation on which the thesis rests. 

In all complete rationalisation of a thesis, then, there 
is always, implicitly at least, one indication used as an 
indication, and therefore abstract. This we shall call the 
Law or Principle. And there is also, implicitly at least, 
a claim that the case or cases spoken of in the thesis 
come under such law. Whether this (the 'minor 
premiss ') be itself an abstract or a concrete proposition, 
it is equally called the Application. The doctrine of 
the Syllogism, whatever other value it may possess, is 
mainly useful, as regards the rationalisation of a thesis, 
for drawing attention to any links that may be missing 
from the chain of complete demonstration. The present 
is not however the best opportunity for discussing the 
details of this operation. In this first general view of 
Proof, it is sufficient to register the assertion (afterwards 
more fully justified; see pp. 212, 300) that Syllogism, so 
far as the said purpose is concerned, is perfectly general 
in its operation, — applies to all Proof whatever, and is 
not, as the beginner is apt to think it, an engine to be 
used in ' Deductive Inference ' merely. 



114 FALLACIES. [Part I. 

As regards Proof, then, the uses of the Syllogism are 
chiefly two : — 

(1) When a person has already admitted the truth of 
a principle and its application, to bind him down to 
every particle of assertion thereby made. In this use 
(as we shall see later) it is an argumentum ad hominem. 

(2) When any thesis, with its reason, is put forward, 
to enable us to supply whatever is wanting to complete 
the Demonstration. We thus apply our knowledge of 
the syllogistic needs, either in order to determine the 
general law under which the special case in question is 
supposed by the assertor to come, and from which the 
thesis is supposed to derive its cogency, — and this with 
the intention of inquiring into the truth of such under- 
lying assumptions : or else (where no principle has yet 
been formulated) in order to force the assertor to see 
what must still be done in order to stop all gaps in 
conclusive reasoning. The mode of these operations will 
be more fully developed in the sequeL 



PART II. 

THE POSSIBILITIES OF EBBOB. 



SECTION I.— BEFOEE PEOOF. 
CHAPTER I. 

INTRODUCTORY. 

Having thus sketched in outline the main facts 
regarding Assertion and Proof which are of preliminary 
importance, we are now at liberty to begin to trace the 
actual bearing of these on the detection of Fallacy, by 
examining in detail the openings at which error may 
creep in. 

When an assertion is first enunciated, the Possibility 
of Error is at its maximum, and we have now to exhibit 
the process by which, step by step, this possibility may 
be reduced. We are only concerned, of course, with its 
reduction to the lowest minimum attainable, not at all 
with the question how nearly the goal may absolutely 
be reached. There will be no harm therefore in con- 
ceding that after Logic has done its utmost, human falli- 
bility remains : only let us protest against the view that 
.since the moon is out of reach there is no sense in trying 
to cultivate the earth. 

It must be remembered further, that since the 



118 FALLACIES. [Part II. 

detection, rather than the total avoidance, of Fallacy- 
is the chief object of our present inquiry, this method of 
diminishing the chances of error is only intended to be 
used for making sure that such and such a fallacy is 
absent. By trying which of the series of possible attacks 
a given assertion or argument can fairly meet, we at the 
same time discover its point of weakness. If it should 
pass our whole examination, we discover, not that it is 
absolutely free from all possibility of error, but merely 
that such possibility must be of the more remote kind 
which for practical purposes we are accustomed to accept 
and disregard. 

In the Introduction, the possible objections to any 
assertion were broadly divided under three heads : — 

(1) The objection to its reality as an assertion, its 
capacity for Proof or Disproof; an objection which seeks 
to condemn the Thesis as such, and without even in- 
quiring what its grounds may be, as containing a mere 
empty shell of assertion, without a meaning : 

(2) The objection that the Thesis is a mere assertion; 
standing entirely alone and without even attempted 
support ; or in other words that nothing has been done 
to remove the burden of proof: and 

(3) That though ' real ' reasons are brought forward 
in support of a ' real ' assertion, such reasons are insuffi- 
cient; which objection is commonly condensed into the 
two words, Non Sequitur. 

The plan here followed then will be to take each of 
these objections in turn, to discuss them by the help of 



Chap. I] INTRODUCTORY. 119 

examples, and also to connect them with the broad 
principles of Logic. And first in order comes the charge 
of Unreality. 

In a former chapter* unreal propositions were divided 
under three heads : — 

(1) Tautologous, or ' essential,' or ' identical ' proposi- 
tions, or 'Platitudes': (Jf already enunciated in the 
meaning of S). 

(2) Self-contradictory, or suicidal, propositions: (J 
already contradicted by the meaning of S). 

(3) The case where any term used in a proposition is, 
from any cause, devoid of meaning. 

In each case, then, it is clear that the meaning of 
the terms employed is the important matter, and that it 
is only so far as such meaning is wanting in clearness of 
conception that this particular fallacy can occur. Defini- 
tion of the terms is accordingly the direction in which 
to look both for means of detecting the fallacy and for 
safeguards against the first of the main objections. 

* See pp. 43-48. f Symbol first employed on p. 51. 



CHAPTER II. • 

THE KINDS OF UNREAL ASSEETION. 

I. Tautology, or Platitude. 

Taking in order the three heads — Tautology, Self-con- 
tradiction, and Meaningless Term, — it may be of service 
first of all briefly to enlarge the explanation above given 
of their nature, — their causes, varieties and results. 

First, then, as regards Tautology. Its causes and 
results are essentially the same as those of the Fallacy 
known as Petitio Principii, or begging the question. 
The assertion itself revolves smoothly in a circle, just as, 
in the latter case, that more complex kind of assertion 
known as an ' argument ' may be seen to do * We render 
the assertion unassailable, by simply postulating ah initio 
(in the definition of its terms) that it shall not be assailed. 
Psychologically, indeed, it may be true that in most cases 
of apparent tautology pure and simple, there is really a 
fluctuation between two assertions (closely similar, per- 
haps, in form), — one real but highly insecure, and the 
other verbal and thereby safe against all attack on the 

* Cf . infra, p. 193 /. 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 121 

score of truth ; and that we use the former when no one 
is looking, the latter only when awkward doubts arise. 
Such, perhaps, would be a fair explanation of what 
George Eliot calls "those undeniable general proposi- 
tions which are usually intended to convey a particular 
meaning very far from undeniable," — examples of which 
are often given in her dialogues, as " He said it did as 
much harm as good, to give a too familiar aspect to re- 
ligious teaching ; " or " The coachman, if he had been 
asked, would have said, though he might have to fall 
down dead the next minute, that property didn't always 
get into the right hands ;" or "There's no knowing what 
may happen before Lady Day." But such cases do not, 
I think, account for the whole employment of these 
empty forms : and where the assertion is purely devoid 
of all forward movement, our acceptance of it as bearing 
a meaning seems to be due to essentially the same slack- 
ness of mental tone that enables us to draw satisfaction 
out of circular proof. Strictly speaking, the shifty 
assertions above noticed belong rather to Ignoratio 
Elencki, — a subject to be discussed later: the fallacy 
being in such cases perhaps, not really that of accepting 
as capable of test or verification a proposition which con- 
tains no real subject-matter for Proof, but rather that 
of asserting one proposition, and believing, or trying to 
establish, another. The chief motive for Tautology 
proper seems to be the desire to say something (or to 
accept any 'explanation' rather than none) on a subject 
of which our knowledge is not deep or exact. Such 



122 FALLACIES. [Part II. 

desire is often coupled with a dim feeling that caution in 
expressing ourselves is necessary : as in a passage which 
may be quoted from a certain Tourist's Guide — "The 
expense of travelling on the continent depends more or 
less on the habits and means of the traveller, and his 
mode of journeying ; and likewise on the rate of charges 
made in the various countries." So much as this might 
have been known without the help of any assertion at 
all, and the belief that it really tells us anything is 
obviously an illusion. 

It must further be noticed that there are occasions 
when a sentence which as it stands may seem to be the 
purest tautology, possesses a real value in spite of 
having, on its own account simply, no capacity for Proof. 
With these we have already made acquaintance, namely 
in the statement of Postulates, whether such Postulates 
are general or special, — ' Laws of Thought/ or definitions 
of given names. When we state the proposition 'A 
is A/ or when we say " A city is a large town possess- 
ing a cathedral," it is certainly true that in both cases 
the J is already contained, to say the least of it, in the 
meaning of the S. But these assertions, when so inter- 
preted, are not theses set up for Proof at all. They are 
merely our means of registering fundamental assumptions, 
whether general or special ; and they pretend to be no 
more than this. Or rather, if in any case they do pretend 
to capacity for Proof, then their real S or J becomes 
a very different one from that which appears on the 
surface. It is conceivable, for instance, that the expres- 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 123 

sion ' A is A ' might be used to convey some such meaning 
as " One fundamental postulate of thought is that the 
meaning of a term is capable of fixation," — a proposition 
certainly not merely verbal : or again " A city is, etc." 
might be used to mean "the ordinary (or the best) 
meaning of ' city ' is, etc." — a proposition whose proof 
or disproof might indeed be difficult but is by no means 
necessarily out of question. These cases, therefore, do not 
affect the rule in any way, and are only worth mention 
in order to bring into greater prominence the difference 
between asserting anything as worthy of credence, and 
merely registering a Postulate in order to let the full 
extent of our assumption be openly known. 

As to the forms in which Tautology occurs, it follows 
from this interpretation of its nature that it is chiefly to 
be found in propositions that profess to be in some way 
explanatory, whether explanatory of names or of facts. 
Thus, a definition may be circular, as where each of two 
contradictories (as ' luxuries ' and ' necessaries ') is defined 
solely by the other, without reference to something 
known independently of both, Or again, we may pretend 
to explain the effect of opium by saying that it has a 
'soporific virtue.' Or again, we may bravely put for- 
ward an abstract proposition (a 'law' or 'principle') 
which on inquiry turns out to need no bravery at all : 
as, for example, when we lay down the law that " we 
ought not to do evil that good may come " — if, as is 
usual, ■ evil ' be defined as equivalent to ' that which we 
ought not to do.' A proposition of this kind is, no doubt, 



124 FALLACIES. [Part II. 

secure against disproof, but only in the same way as a 
dumb man may be called secure against speaking falsely, 
or as a suicide may be called secure against the less 
voluntary kinds of death. 

Passing by the grosser cases of Tautology, however, 
which have been sufficiently illustrated in the earlier 
chapter,* the chief problem for practical interest, in this 
danger as in all, is as to the borderland between what is 
fallacious and what is valid: the drawing of the line 
that separates tautology from real assertion. The great 
difficulty in deciding in practice whether a giving assertion 
is tautologous or not, flows of course from the fact that, — 
outside names with a purely technical or artificial mean- 
ing, as ' triangle,' or ' city/ or ' fee simple,' — the meaning 
of a word is never completely fixed, but is subject to 
fluctuations, slow or rapid, gradual or irregular. If 
there were some competent authority to which appeal 
could be made in all cases, the fallacy of taking mere 
platitude for real assertion could no doubt be pointed out 
in any case with ease: we should simply turn to our 
dictionary and compare the meanings there given of the 
words employed. But as yet, unfortunately, no such 
universal authority exists. 

In the first place, when we speak at all of ' the ' 
meaning it becomes important to decide ivhich meaning 
is the object of our inquiry. For the same word may at 
the same time possess several different hinds of meaning, 
to say nothing of the different shades (or amount) of 

* Part I. Chap. IL 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 125 

meaning which it may bear to each individual who 
employs it. "We may distinguish, for instance, as possible 
objects of inquiry : — 

I. The meaning that the word does bear, 
(a) to ' most people ' — vaguely estimated : 

Q3) to some particular person or class of persons, 

(1) under the impression that it is the 
' correct/ or the only, meaning : 

(2) As a postulate ; i.e. as a special meaning 
consciously put upon it as such by the 
speaker: 

II. The meaning that the word ought to bear, 
(a) for convenience in classification, etc. 

(/3) on historical, etymological, or other grounds. 
It seems, therefore, not quite satisfactory to say with 
Professor Bain * that "all newly discovered properties are 
real predications on their first announcement, although 
immediately on being communicated they become verbal." 
In one sense, no doubt, this is perfectly true ; but the 
expression quoted needs to be interpreted with care. If, 
e.g. a chemist were to announce that some hitherto sup- 
posed element is really decomposable, we can hardly 
suppose that by the fact of such mere announcement all 
the rest of the world is at once prevented from investi- 
gating the matter : that the assertion has become a mere 
truism, that to doubt it is henceforth impossible and to 
test its material truth absurd. So much may no doubt 
be safely said as this, — that our ignorance or forgetfulness 

* Deductive Logic, p. 70. 

7 



126 FALLACIES. [Part II. 

of the truth of a proposition, and hence our power of 
viewing it as questionable, is what makes it real to us. 
But the point of first importance to notice and remember 
is, that as a rule when using a name we can only have 
before us quite a small part of its total meaning, and that 
we do not habitually remember even all we can : we only 
remember, or only keep prominently in mind, quite a few 
of the propositions, regarding the S in question, which 
we ' firmly believe ' to be true, and as a rule those last 
discovered are least regarded as forming part of the mean- 
ing of the name. Hence we may repeat, and with a real 
meaning, propositions expressing even facts discovered 
long ago, — as that the Earth is round, or that sunrise and 
sunset are due to its revolution. For purposes of Proof 
the important distinction lies solely between assertions 
capable of denial with a meaning, and those which to 
deny would contradict the postulated meaning of the 
name employed as S. 

In our sense, then, the reality or verbality of a pro- 
position is not determined once for all by the fact asserted 
having been already discovered, or even being already 
generally known ; but varies with the purpose for which 
such proposition is now in the given case employed : i.e. 
it depends upon the prominence of the already-known 
fact in our minds at the time of using the name or names 
forming the S of the proposition. So far as the fact, if 
known, is remembered, so far is the proposition verbal, 
and any attempt to prove it involves of course a circle in 
our thoughts : so far as the fact is hidden from memory 



Chap. II.] THE KINDS OF UNHEAL ASSERTION. 127 

so far there is real matter for Proof. If rotundity enters 
into our notion of the Earth, then it is obviously futile 
to ask whether the Earth (so understood) is, or is not, 
round. But that many people find no difficulty in keep- 
ing the attribute of rotundity entirely absent from their 
notion of the Earth, habitually building up that notion 
piecemeal from remembered landscapes, if it may not be 
inferred a priori, at any rate may be surmised from 
the existence of the numerous pamphlets — long post- 
Copernican — catalogued in De Morgan's Budget of Para- 
doxes. And accordingly the assertion of the Earth's 
rotundity is capable of being ' real.' 

How then does Definition help in deciding whether a 
given proposition is or is not tautologous ? If no absolute 
and fixed meaning ever exists (except in the case of 
certain technical terms) how can we establish, in other 
cases, any general test of tautology ? 

The most we can really do is to bind the assertor 
down to a special definition of his own ; to ask for the 
special meaning which he intends to keep in view. The 
meaning of a word is much like the " market value " of 
an article, — a matter to be settled between the parties 
concerned. We can, it is true, satisfy our sense of justice, 
or of general responsibility to our neighbour, by accusing 
him of ignorance of the ordinary meaning (or, if we are 
very self-confident, of the best meaning) of the words he 
uses : but such an accusation is a totally different one from 
that with which we are here alone concerned. It affects, 
no doubt, our opinion of the speaker's general level of 



128 FALLACIES. [Part II. 

common-sense or of education, but not at all the question 
whether or no the assertion as made and intended admits 
of Proof and Disproof. It should be remarked, more- 
over, that there is often considerable difficulty, even in 
this way, in obtaining valuable results. People do not 
as a rule enjoy being cross-examined, — or only in the 
rare cases where both assertor and questioner are simply 
anxious to avoid mistakes ; where the claim to oracular 
dignity on the one side, and the spirit of mischief or 
obstruction on the other, are wholly wanting. 

For besides the real danger of platitude, there is an 
opposite danger to be avoided, namely that of unduly 
and vexatiously stopping an argument to have the terms 
explained. Without wishing exactly to defend those 
who made Socrates drink poison, one still cannot help 
recognising that there is a limit beyond which the laud- 
able desire for definiteness loses its value and becomes a 
hindrance and a snare. There is something so fatally 
easy in the attitude of a sceptic or mere questioner. 
Any child can keep demanding explanations, any man 
sufficiently stubborn can delay the most important truth 
by pretending not to understand its import. An obstruc- 
tive policy of this kind requires no great intellectual 
power, and, when adopted solely for obstructive pur- 
poses it demands, as much as anything, a rule of urgency. 
Life is not long enough for exhaustive explanations. 

Here at the outset, then, we find two opposite dangers, 
and no exact rules can be given for avoiding either. The 
most that practical Logic can do is to set up an ideal of 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 129 

clearness and precision, and to demand that where we 
fall short of it we shall show fair cause for doing so, — e.g. 
the need for saving time or for getting work accomplished. 
The assertion that explanation ought in a given case to 
be unnecessary can of course be proved like any other. 

II. Self-Contradiction. 

Whereas Tautology is chiefly a failing of feeble or timid 
folk, self-contradiction is a danger to which the rash and 
immature seem specially liable. As above remarked, 
it is more often a fault in expression than in thought. 
Half the Irish ' bulls ' (an Irishman once explained to me) 
are merely expressions that are too epigrammatic for 
the slow-moving Saxon mind. And of course, where this 
is the case, such assertions can always be translated into 
sober English at the cost of a little trouble or prolixity. 
If at least, in any case, they cannot be so translated, we 
have obviously no other means of getting their meaning 
clear in order to bring them to the test. It is often as 
painful to translate an epigram as to explain a joke, and 
a good example of such translation would be rather hard 
to find. May we say that when an orator once declared 
that his party had " a majority in everything except 
numbers," he himself was fully aware of the verbal con- 
tradiction, and only intended smartly to rap the knuckles 
of the god Majority ? The answer would depend upon 
our knowledge of the speaker's mental habits, rather than 
on any analysis of the words alone. 



130 FALLACIES. [Part II 

But paradoxers (as De Morgan called them), though 
sharing with some great discoverers the honour of being 
despised at first by Common Sense, do not always re- 
semble pioneers in other and more essential points. There 
can be no doubt that a good deal of self-contradiction 
is in fact rather due to hastiness or crudity of thought 
than to any nobler origin. As Mr. Herbert Spencer 
notices, " the ability of men to compromise between con- 
flicting beliefs is very remarkable — remarkable, at least, 
if we suppose them to put their conflicting beliefs side 
by side ; not so remarkable if we recognise the fact that 
they do not put them side by side." Mere forgetfulness 
of our definitions may lead us into inconsistency just as 
well as into repetition: the main difference being that 
whereas one element among the causes of tautology is 
often the sense of the need for caution, in self-contra- 
diction this sense seems to be wholly wanting, — often in 
fact to have its place supplied by a reckless desire for 
some new thing at any price. 

Of contradiction between S and J (as distinguished 
from contradiction within a term, — which comes more 
properly under our next head) it may be said, first, 
that its danger depends to a great extent upon dilution. 
The simpler and shorter the proposition, the less easy 
is it to find really dangerous examples. " Twice two 
are five/' for instance, runs no risk of being mistakenly 
accepted for a real assertion ; and in treating the subject 
for our purposes we may in the first place cut off 
from consideration the cases which are so broad and 



Chap. II] THE KINDS OF UNREAL ASSERTION. 131 

evident as to amount to a mere jest. Self-contradictions 
of this sort are endless, from the heaviest scholastic 
puzzle to the latest and lightest French or American 
comic item ; and though these may be capable of pro- 
viding amusement, they are not likely ever to lead to 
serious error. It follows, however, from our extended 
view of what constitutes a proposition, that any two 
(or more) separable assertions, if intended to be taken 
together, may be viewed as one whole proposition ; 
and that therefore we may have a case of unreality 
even where there is considerable interval between the 
conflicting assertions. In this way a writer, for example, 
may contradict himself plentifully in the course of a 
book, the book as a whole attempting to pass off unreal 
assertions upon the reader, though the separate items of 
information may be real enough, and only half of them 
false. But here again the self-contradiction is com- 
paratively easy to detect, A more difficult and subtle 
form of the fallacy arises in the case where no assertion 
is expressly made, but where a question is raised and 
debated as if an alternative answer (yes or no) were 
possible, when in fact one of these answers would be a 
tautology and the other consequently a contradiction. 
As an instance of this may be quoted the question ' Can 
one individual be at the same time a different in- 
dividual ? ' — a case which one would have thought too 
glaring even for use as an example, if it had not been 
discussed at some length and with more or less of 
genuine perplexity in actual writings. 



132 FALLACIES. [Pabt II. 

Here, in fact, we begin to get a glimpse of the more 
serious difficulties in detecting and avoiding this kind 
of fallacy. Speaking broadly, we have seen that self- 
contradiction may be due to two, almost opposite, causes, 
— mere carelessness, on the one hand ; and on the other 
hand all that may be included under the name 'epigram,' 
a scale that may be made to reach all the way from simple 
impatient condensation of a sentence, up to the most 
praiseworthy attempts to rise above the artificial barriers 
of language. Inconsistencies of this latter kind cannot 
always be laid to the account of light-brained ' nihilism > 
of thought, but are rather due to the spirit of deep in- 
quiry, casuistry, or over-carefulness. And the form in 
which the real danger oftenest appears is, as just said, 
the raising debate upon unintelligible questions. 

We may, then, very briefly dismiss from consideration 
the simpler kind of self-contradiction, since here there is 
only one side to be considered. Every one will probably 
admit that mere carelessness, or confusion of mind, is 
a thing to be on the whole avoided, and only requires 
to be pointed out ; which may as a rule be very easily 
done. Thus when Bishop Butler, in his 'Analogy/ re- 
marks that where there is the slightest preponderance of 
probability, prudence requires us to act accordingly, and 
then goes on to say that in questions of great consequence 
we have to be content with probabilities even loiver than 
this ; it is not hard to see that the joint assertion is of 
much the same nature as the saying that " One man is 
as good as another, — and better." So too when a writer 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 133 

on Ethics laid down as an inducement to unselfish- 
ness the rule that "the less we think about being re- 
warded, the better for us," it was probably a mere want 
of consistent thought which led him to overlook the fact 
that he was telling us in the same breath to regard and not 
to regard consequences to ourselves.* Such slips are 
however of very frequent occurrence, especially when our 
case is weak. 

But the other source of inconsistent thought con- 
stitutes a standing difficulty. Nor does there seem to 
be any ultimate and quite satisfactory escape from it. 
It depends upon the real uncertainty of the line between 
a given term and its contradictory: the old standing 
difficulty, commonly known by the name Sorites (and 
more anciently called Soros), — the difficulty of getting 
a truly ' scientific frontier ' for the names we use. Where 
there is gradual change from one state to another, or 
where two opposites, however unchanging, may be 
viewed as different in kind only through being widely 
different in degree, how are we to fix the line between A 
and not-A? Where, for example, is the line between 
'nation ' and ' tribe/ between ' solid ' and ' liquid/ between 
'house' and 'cottage V Or how much money makes a 
man a ' capitalist ' ? 

The deeper we push inquiry into the exact meaning 
of any given name, the more certain it becomes that 
sooner or later we shall find ourselves approaching the 
main quicksand of language, — the fact that words neces- 

* Unless indeed it was merely intended as an argumentum ad homineni. 



134 FALLACIES. [Part II. 

sarily postulate definiteness of outline, while as a fact 
complete definiteness of outline does not exist in Nature. 
The line dividing each class from its nearest neighbour is 
in some cases (e.g. between infancy and full age, at law) 
purely and confessedly a contrivance of our own; in 
other cases (as between ' good ' or ' tall ' or ' strong ' and 
their contradictories) purposely left vague because the 
phenomena either do not admit of, or do not for most 
purposes require, numerical precision ; in other cases (as 
between kinds, and even varieties, in Nature) is pro- 
visionally useful until doubtful instances shall arise. But 
it is important to remember (1) that in all cases the line 
is so far an artificial one that it is we who have made 
and applied the names, and very often mistakenly, for 
purposes of our own; (2) that in all cases the line 
professes to be 'length without breadth,' while as a 
fact there always remains a doubtful margin.* The gap 
between the opposed classes is infinitely divisible, is 
subject to constant subdivision as time goes on, and, 
though it is being gradually narrowed away and its exact 
position altered by the acquisition of new knowledge, we 
can never know that the furthest subdivision is reached. 
A notable example is afforded by the breaking down 
of ancient barriers that is even now taking place in 
all departments of Natural History as the development 
theory becomes more fully understood : one of* the best- 
known problems, for example, that has lately risen into 
high importance, being — If ' man ' has directly descended 

* Cf. Bain : Logic, bk. iv. chap. i. sect. 3. 



Chap. EL] THE KINDS OF UNREAL ASSERTION. 135 

from ' beast/ at what point in the history of such descent 
does man, as such, emerge ? Various accounts have been 
given of man's differentia from other animals; among 
the most popularly known of which, perhaps, are that he 
is rational, has the power of laughing, the use of language, 
or of tools, or the practice of cooking his food. So far, then, 
as these points are themselves definite and clearly under- * 
stood, so far but no further will the employment of any 
one of them as differentia bring clearness into our notion 
of 'man.' In other words, we may (and, for the purpose 
of attaining the highest possible degree of accuracy, must) 
push inquiry into definitions back and back until we 
reach quite firm and undisputed ground. Thus it may be 
asked what constitutes rationality ? Does a dog reason, 
however hastily, when having once been scalded he ever 
afterwards dreads cold water ? Is a sense of the ludicrous 
absolutely wanting in the monkey, and always present 
in the man ? What is language but vocal sounds con- 
veying a meaning, and have not many brutes the use of 
these ? And so on. One definition rests upon another, 
and inherits the defects as well a3 the virtues of its 
ancestry : if the first link in the chain is faulty all the 
rest must suffer to that extent. Above all, the difficulty 
shows itself, as just remarked, in that the further back 
we trace man's history the less we find of all these dis- 
tinctive qualities — the more imperfect reason, sense of 
humour, language, tools and cookery : and the inference 
becomes to many people irresistible, that at a still earlier 
period these attributes were wholly wanting, or if present 



136 FALLACIES. [Part II. 

in the germ, at least as uncertainly recognisable as they 
now are in the case of ' beasts.' At what period, then, 
precisely, did man first deserve the name ? If it be ob- 
jected that owing to the scantiness of the data, man's 
remoter history is merely conjecture, we will dispense 
with this instance altogether, and instead of it take 'man' 
defined as a c grown-up child :' at what exact period can 
the epithet ' grown-up ' be applied to him ? Most of us 
have in our own case a lively remembrance of the diffi- 
culties in fixing this definition. 

It is, however, not our purpose here to attempt to do 
full justice to the difficulties of language, or to do more 
than point out vaguely where some of them lie. "Words 
and their meaning are altogether full of unsuspected 
dangers, but to treat those dangers usefully demands a 
treatise to itself. When we consider how language has 
grown, thrown up at first by savage ancestors living from 
hand to mouth, framed to meet their simple needs and 
to express the results of their desultory, unassisted obser- 
vation ; altered here and there to compromise with the 
growing knowledge, but often refusing stolidly to admit 
past errors, and merely adapting itself by some circuitous 
fiction to the new-fangled notions (as 'planet' now 
means no longer a wandering star as viewed from the 
Earth, but a body moving round a sun — thus including 
the Earth itself); the ignorance of one age taking root 
and hampering the efforts of the next to see things more 
nearly in their true relations ; always in fact lagging a 
little behind discovery, and delaying the birth of the 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 137 

best ideas that are taking shape ; when we consider all 
this, the wonder is, not that confusion frequently occurs, 
but that any consistent expression of our thoughts is 
possible. In fact it is probably not too much to say that 
we can never be quite secure from all taint of this error. 
There is consolation, however, in the fact that a good 
many of our needs too are rough and ready, and that a 
good deal of what we say is definite enough for the 
ordinary purposes of life. Where any practical harm can 
be traced to this difficulty, one business of the logician is 
certainly to point it out ; and to him it may even be to 
some extent satisfactory to recognise that there is plenty 
of work to do. 

In the case of self-contradiction, as in that of 
Tautology, much may no doubt be done by inquiring as 
to the special meaning put upon S by the speaker. But 
the artificial character, and possible unsatisfactory results, 
of this safeguard rise here into greater prominence, since 
here attention is attracted rather more directly and openly 
to the defining line itself; and it must be admitted that, 
as things are, it is often unfair (or let us say, unpractical 
and obstructive) to press for exactness of line. There is 
some value even in vague assertion, — at least where, as 
often happens, nothing better can be obtained. While 
allowing that until the contradiction is removed by some 
means, Proof or Disproof in any strict sense is impossible, 
it is well at least to recognise that self-contradiction is 
not necessarily so flat and unprofitable as Tautology. 
Often, of course, it flows from mere love of paradox, often 



138 FALLACIES. [Part II. 

also from haste or inattention : but sometimes it will be 
found that existing language, and not the speaker, is 
most to blame. And on such occasions the paradox may- 
usual ly, with sufficient patience, be translated into a real 
assertion ; or else may be accepted easily, and tasted, in 
an after-dinner frame of mind. 

III. Meaningless Term. 

The third class of verbal assertions is far less simple 
in character than the two just discussed. To treat it 
fully, in fact, we should have to exhaust the question as 
to the limits of our power of defining effectively: and 
this can, of course, not be attempted. There may, 
however, be some use in showing where that difficulty 
lies. 

But in the first place any term may be meaningless 
either (1) simply, — i.e through want of definition; or 
(2) by self-contradiction, — as where, in a complex term, 
opposed meanings are verbally combined. 

This second case is so closely allied to the kind of 
verbal assertions discussed in the preceding section, that 
not much remains to be said. The difference in fact is 
chiefly a grammatical one ; instead of saying ' A belongs 
to the class not- A, with the differentia B ' (e.g. ' man ' 
belongs to the class 'not-man' with the differentia 
'evolved' or 'Life is a gradual death') we here say 'A 
which is not- A is B ' (e.g. ' Unconscious hypocrites are 
always the worst') or 'B is A which is not-A' (e.g. 'A 



Chap. IL] THE KINDS OF UNREAL ASSERTION. 139 

continent is an island which, through mere difference of 
degree in size, is not an island ; ' which assertions might 
be resolved into double, or joint, propositions, one member 
of which contradicts the other. But there is some use 
in treating these self-contradictory terms separately, 
since the junction of incompatible members into one term 
has, on occasion, certain excuses which seem to apply 
more specially to this case than to that of contradiction 
between S and ^. In the first place, when a term has 
from any cause lost its original meaning, there is of course 
no contradiction in combining with it another which 
contradicts the original meaning but leaves the acquired 
one free. We may, for example, use the expression ' bad 
goods/ or again 'dry humour,' with complete reality of 
meaning : nor, in a sentence such as " They overlooked 
the boundless field that was before them within the 
legitimate limits of the Science," does the solecism in- 
validate the assertion made. Conversely, too, a legitimate 
excuse for such propositions may be simply the desire to 
call attention to the wrong use of a name, as in 'The 
present Government is no Government at all,' or, ' If your 
facts are false, your inference is useless.' And in the 
second place, though such an expression as a 'round 
square ' would be generally ruled out of court as meaning- 
less, it seems to be quite allowable to speak of an ■ irre- 
gular square,' or of ' a globe which is not quite globular. 
In two distinct cases under this head there is a recocr- 
nised license to combine terms really contradictory; — 
(a) where the qualification is only slight, and the ex- 



140 FALLACIES. [Part II. 

pression is intended to be merely rough and ready, — as 
in the instances just given; and (6) where the intention 
is to indicate a mean between opposed notions, as in 
' Liberal- Conservative ' or 'blue-green colour/ or 'dead- 
alive/ 

Considerable caution, therefore, should be exercised 
before accusing a complex term of being really suicidal : 
so much must be allowed. But when all possible ex- 
cuses have been made, there remains a residuum of 
cases which are purely fallacious, and which are by no 
means so rare as might be supposed. No doubt it is 
chiefly through our power of fluctuating unconsciously 
between two different beliefs that these ' beliefs ' justify 
themselves to the believer: each separately is seen to 
convey a real meaning, and it seems to be dimly supposed 
that since each is a positive belief (how many errors 
that word ' positive ' has to answer for !) the total result 
cannot in the nature of things be a non-entity. Indeed, 
this defence has been sometimes almost openly put for- 
ward. No doubt where the sole object is to find some 
form of words ' true ' which is at the same time admitted 
to be ' incomprehensible ' we have a contradiction already 
as a starting-point, and it is perhaps only natural that 
others should be needed to support it: but natural or 
not, such a process is apt to confuse people's minds as to 
what is meant by belief at all, and to blunt the edge 
of their conscience towards themselves. Possibly this 
is one reason why the habit of delighting in mysteries 
retains its hold so long. 



Chap. II.] THE KINDS OF UNHEAL ASSERTION. 141 

Turning now to the case where a term lacks mean- 
ing for want of being defined, we may distinguish in the 
first place the two varieties : — (a) where the term simply 
has not yet been defined by the speaker ; and (b) where 
a definition has been given, indeed, but one which does 
not really explain. 

The remedy in the first of these cases is of course 
simple enough ; in fact, it only needs mention by way of 
introduction to the second case. It is clear that when we 
say 'x is good,' or ' every man is x' there is no subject- 
matter for proof until the meaning of the x is declared : 
and that if it can be declared this had better be done as 
soon as possible. 

What then are the limits to our power of giving names 
a ' meaning ' ? And how can we avoid false security in 
the matter ? 

Since for definition it is necessary to refer to some 
higher class (Genus), it is clear in the first place that the 
most general notion of all — whatever that may be — 
cannot in strictness be defined. A summum genus, 
indeed, is usually taken to mean something much less 
extended than the one highest genus of all, namely to 
mean the highest in any given series, — which series may 
of course be a quite arbitrary selection of our own. Thus 
in the series 'Mineral, rock, stratified rock, limestone,' 
'mineral' would be the summum genus, although a higher 
class, namely ' material substance,' might easily be added 
to the series, and beyond that again the class ' nameable 
thing.' It is therefore incorrect to say that no summum 



142 FALLACIES. [Part H. 

genus is definable, — unless we are speaking only of the 
one highest of all ; or unless we consider the inexplicable 
nature of this ultimate notion to vitiate all other general 
names, since all may be traced up to it. In absolute 
strictness there seems, in fact, to be no escape from this 
difficulty. It is, no doubt, always theoretically lawful, 
though not always practically expedient, to push inquiry 
into the meaning of a name back into Metaphysics, — just 
as it is possible to demand any other kind of ultimate 
explanation. Any objection to such inquiry can only 
rest on the plea of practical needs ; and it is not easy 
to say how far such plea itself will bear stretching, — for 
who is to decide that our view of practical needs is 
sufficiently long-sighted ? 

It certainly seems as if — to quote Prof. Bain * — " the 
highest universe of all must contain at least two things, 
mutually explaining," and that our highest definitions 
must accordingly be merely circular. Short of this 
ultimate circle, or assumption, however, we can of course 
take care to avoid all narrower circles in defining. 

The only other kind of delusive definition that need 
be noticed in this connexion is that sometimes called 
' defining ignotum per ignotiws? as where a writer 
explains the meaning of ' miracle ' to be " an abnormal 
exercise of constitutional sovereignty on the part of the 
very divine Ego, in respect of the subsistere of the cos- 
mical selfhood of the metamorphosed Non-Ego." Here 
we can of course either take the requisite pains to make 

* Deductive Logic, p. 59. 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 143 

out the real meaning intended, or we can wait for some 
more easily intelligible information. But until such 
additional process has been performed, any proposition 
containing f miracle ' as S or J remains obscure. 

As regards the whole question of the need of definition, 
it should be remarked that the mere fact that the terms 
have not yet been defined, or have been imperfectly 
defined, does not of itself necessarily deprive an assertion 
of all ' real ' meaning. If this were so, indeed, the con- 
veying of information would be even a more lengthy and 
troublesome process than at present. It is only when 
the need is felt, as such, by the person addressed, that 
the assertion can fail, in this way, on the ground of 
unreality : for where the audience put a wrong meaning 
(i.e. one not intended by the speaker) on the terms 
employed, there is misunderstanding, perhaps, and there 
may be fallacy on one side or the other ; but inasmuch 
as the audience do put some meaning on the assertion, 
it is real to them. 

IV. Unreal Assertion: Concluded. 

We have seen, then, that against the fallacy of takino- 
an unreal proposition for a real one, the remedy in all 
cases is to be found in definition of the terms employed ; 
and that everything depends upon the special meanino- 
given to them by the assertor; since any apparent 
tautology or contradiction may have its fallacious 
character removed, any unknown meaning may be made 



144 FALLACIES. [Part II. 

known (within the limits indicated above) by such 
special explanation. We have seen, too, that Tautology 
is intimately connected with the fallacy of Petitio Prin- 
cipii, or circular proof, while self-contradiction, except 
when merely used to condense a real proposition, is really 
a case of inconsistency, — sometimes due to mere careless- 
ness, sometimes to the fact that lines of distinction in 
nature, on the preservation of which all consistency 
depends, are artificial contrivances of our own, which do 
not exactly fit the facts, but can only be roughly justified. 
And as regards explanation of the meaning of a term, we 
must admit, I think, that there is a point beyond w T hich 
any attempted explanation becomes unreal ; and, hence, 
that the distinction between reality of meaning and mere 
verbality has a value only so long as we keep away from 
the deepest difficulties. 

Before leaving the subject, there are one or two 
points to be noticed as regards unreal assertion in 
general rather than any special form of it. First of all 
it may be well to distinguish clearly between verbal 
assertion (i.e. tautology) and verbal questions, — as where 
a disputed point is said to be "merely a question of 
names." Whately has expressed as concisely as any one 
the distinction between verbal and real questions, — "If 
it . . . appear . . . that the opposite sides of a certain 
question may be held by persons not differing in their 
opinion of the matter in hand, then that question may 
be pronounced verbal, as depending on the different 
senses in which they respectively employ the terms. If, 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 145 

on the contrary, it appears that they employ the terms 
in the same sense, but still differ as to the application of 
one of them to the other, then it may be pronounced 
that the question is real, — that they differ as to the 
opinions they hold of the things in question." " If, for 
instance," he continues, " two persons contend whether 
Augustus deserved to be called a 'great man,' then if it 
appeared that the one included under the term ' great ' 
disinterested patriotism, and on that ground excluded 
Augustus from the class, as wanting in that quality, and 
that the other also gave him no credit for that quality, 
but understood no more by the term 'great' than high 
intellectual qualities, energy of character, and brilliant 
actions, it would follow that the parties did not differ in 
opinion, except as to the use of a term, and that the 
question was verbal. If, again, it appeared that the one 
did give Augustus credit for such patriotism as the other 
denied him, both of them including that idea in the term 
great, then the Question would be Real." In short, there 
may be a real assertion made about a name just as well 
as about any other S ; and often this is made in so con- 
fused a fashion that there is difficulty in seeing what is 
intended. Of course, where two persons really agree 
about the actual qualities possessed by Augustus, and 
one says, ' these qualities, good and bad together, on the 
whole entitle him to a place in the class of great men,' 
while the other says ' precisely the same qualities do not 
entitle him to the name,' the former really asserts, while 
the latter denies, that (in their respective opinion) the 



146 FALLACIES. [Part II. 

best meaning of ' great ' includes that particular mixture 
of qualities which both allow to belong to Augustus. 
But the difficulty in the matter usually flows from the 
fact that neither party to the discussion knows very 
clearly either what qualities he does actually suppose 
Augustus to possess, or what qualities he does actually 
include within his meaning of the name. All that we 
are concerned to notice, however, is that the confusion — 
if confusion there be — is not that of mistaking an empty 
form of words for a real assertion, but of mistaking one 
real assertion for another. The question whether or no 
a given definition is a good one may indeed be properly 
called a ' verbal question,' but it is clearly not a question 
without meaning or without important consequences. 
An assertion about the meaning of a name, when under- 
stood as such, is not a verbal assertion in the sense of 
being incapable of Proof. 

Another question, of side interest, may be just 
mentioned for dismissal. Since the reality of an asser- 
tion is coincident with its capacity for Proof and Dis- 
proof, are we to distinguish degrees of ' reality ' according 
to the completeness and definiteness of the possible test to 
which different real assertions are liable ? It is obvious 
that assertions vary very much in this respect. Is, for 
example, the assertion, ' You will find him in the next 
room/ more real (because more capable of being brought 
to a conclusive test) than an assertion regarding the 
details of the distribution of ice over Europe during the 
last Glacial Epoch ? Certainly not. As I have intended 



Chap. II.] THE KINDS OF UNREAL ASSERTION. 147 

to use the term ' real ' throughout, there are no degrees 
in it, — no standing-room between real and unreal. If it 
be desired to express the distinction just spoken of, there 
are other words, — such as 'verifiable' — which would 
answer the purpose better. By ' capacity for Proof and 
Disproof was not meant the degree of ease or certainty 
with which the assertion might be established or over- 
thrown, but the mere fact that there is at least no absolute 
impossibility, in the assertion itself, that relevant evidence, 
weak or strong, should ever be produced. The unreality 
of a proposition is not in any way connected with the 
mere inaccessibility of Proof and Disproof, but with their 
total inapplicability. To establish or demolish some 
'real' hypotheses may be as difficult as to establish a 
dynasty, or to remove a mountain ; but to support or 
disprove an unreal proposition is as impossible as to 
support a dead Pretender, or to remove a hat from a head 
already bare. 



CHAPTER in. 

THE BURDEN OF PROOF. 

Supposing a Thesis sufficiently free from the taint of 
unreality, two other main objections or opportunities for 
attack remain And the first of these, as already said, is 
the objection that no proof has been attempted, — that 
the thesis is a mere assertion, standing entirely without 
support or evidence. 

Evidence, it should be at once noticed, is not here 
used in the more restricted sense that would contrast it 
(e.g.) with ' authority ' or with ' hearsay ; ' but as broadly 
as possible, so as to include the weakest kinds of evidence 
as well as the strongest. It is just as truly an argument, 
for example, however fragile, to claim that a given 
assertion is true because it occurs in a certain book, or 
was made by a certain person, as any other ' reason given 
for belief would be. The contrast between supported 
and unsupported assertions does not depend on the 
strength or weakness of the reasons, but on whether 
or not reasons of any kind are given. The full question 
as to the burden of Proof is sufficiently confusing in 



Chap. IIL] THE BURDEN OF PROOF. 149 

itself, without our introducing further entanglements 
prematurely. 

Two cases are to be distinguished: — (1) Where an 
assertion is put forward simply as ' self-evident,' or free 
from all need of Proof; and (2) where the assertor 
supposes (or tries to lead his audience to suppose) that 
his sole concern as assertor is to frustrate, one by one, 
attempts at Disproof made by some one else. 

The first case need not detain us long. For while 
fully admitting that without some ' self-evident ' truths, 
no Proof of any assertion would be possible, it can hardly 
be denied that what seems self-evident to one person 
may seem to another to stand much in need of external 
support. And since the whole meaning of the Need of 
Proof is need as felt by the audience, and not as the 
assertor happens to think the audience ought to feel it, 
they, and not he, must be the arbiters. If the assertion 
is not to them self-evident, they are under actual dis- 
ability to believe it until external evidence is produced. 
I am speaking, of course, of genuine belief, intelligent 
and rational, and not of mere voluntary acceptance of a 
formula, as an act of obedience or otherwise. It may, 
indeed, often happen that the grounds are so numerous, 
or have been so long forgotten through disuse, that their 
production would be difficult or impossible. Deep-lying 
and complicated beliefs, especially when illumined by 
emotion, or when the more physical element in them 
is prominent, are very liable to this difficulty, — the 
beliefs (e.g.) on which our likes and dislikes of persons 
8 



150 FALLACIES. [Part II. 

or of systems, or of courses of action, are founded. But 
none the less unsatisfactory must such beliefs remain to 
an audience not already convinced, until the grounds 
can be openly brought forward and examined : and our 
concern is, of course, entirely with the point of view from 
which the assertion is still a thesis, and not with that 
from which it is a firmly established conclusion. Until 
the grounds can be examined no test is possible: the 
assertion may or may not be true, for all the audience 
can say. Against the honest objection, - This is not self- 
evident to me,' there is clearly no appeal ; and no remedy 
except through the production of real external evidence. 

The second case, however, is far more complicated; 
sufficiently so, in fact, to have notoriously confused the 
mind of no less a logician than Archbishop Whately. This 
is another of the numerous cases where statement is easy 
but application difficult, and where the whole practical 
value depends on the application. Stated shortly, 
the fundamental rule is that "He who asserts must 
prove;"* and so long as an assertion is undisputed, 
difficulty cannot arise. But the chief source of real per- 
plexity lies in attempting to keep a clear line between 
denying a thesis, and merely reserving judgment,*!* or 

* Even in Law this maxim seems to be fundamental. Cf. Sir Jas. 
Stephen's Digest of the Laiv of Evidence, 3rd ed. pp. 100 ff. "The 
burden of proof as to any particular fact lies on that person who wishes 
the Court to believe in its existence" (art. 96). See also Articles 93 
and 95. 

t Hence De Morgan and others have preferred to treat displacement 
of the burden of proof as a case of Ignoratio Elenchi. See also the 
examples at p. 188 of this book. 



Chap. Ill] THE BUKDEN OF PROOF. 151 

between disputing an argument and merely asking to 
have it expanded and made satisfactory. This, at 
least, is one of the points at which confusion is in the 
first place most apt to creep in. It is obvious that an 
unsupported assertion may or may not be true, and it 
should be carefully noted that the absence of produced 
evidence, — or even the absence of the possibility of pro- 
ducing evidence, — is a very different thing from Disproof. 
Where nothing is said either for or against a thesis, its 
truth simply remains an open question; and where 
nothing can be said, the doubt is only more permanent in 
character, not otherwise more triumphant. The objection, 
'This is bare assertion/ does not attack directly the 
truth of the assertion in question, but attacks the sup- 
position that such truth is as yet established. Hence 
assertions which are confessedly mere suggestions escape 
unscathed, since all the harm which the doctrine of the 
burden of proof can do to them is done already, and 
willingly, by their assertor himself. It is only where 
an assertion is definitely made that the grounds of belief 
can be demanded with any meaning. 

The simple statement of the rule, that "he who 
asserts must prove," needs, however, certain explanations 
before it can be accepted in its entirety : and the best 
way to bring these forward seems to be by pushing the 
simple rule into its extreme cases. In the first place, 
then, if the burden of proving lies always on him who 
asserts, it is clear that whoever asserts that a thesis is 
false must accept a burden too: and also that he who 



152 FALLACIES. [Part II. 

asserts a reason as sufficient, or claims that it is certainly 
insufficient, is in exactly the same position. These three 
cases do not present much difficulty, and will, I think, 
be readily admitted by all. 

Suppose, for example, I assert some article of popular 
faith, — such as that women ought not to enter the 
learned professions ; my audience may either accept the 
assertion offhand, or deny it offhand, or be content to 
ask for reasons. In the first case the burden passes 
simply unnoticed. In the second case, the audience, as 
assertors accept a burden of their own. In the third 
case the burden rests on me, just as it would if I pro- 
claimed the most startling novelty. For the doubt may 
be suggested that though widely believed, the assertion 
is possibly without secure foundation. That is to say, 
two courses are now open to me — unless my audience 
are unusually feeble disputers — either to take my stand 
on the bare unsupported assertion, and so leave my 
questioner certainly unconvinced ; or else to attempt to 
remove the burden by producing the best available 
reason. If I adopt the latter course, it is clear that 
any permanent removal of the burden depends on the 
strength of the evidence brought forward. But the 
difficulty is, that at every stage of an argument the line 
between interrogation and flat denial is often hard to 
preserve, and a sophist, when pushed by awkward ques- 
tions, will always try to shift the burden upon his 
questioner. Thus, I may perhaps argue, in favour of 
women's restrictions, that "one needs to know that a 



Chap. III.] THE BURDEN OF PROOF. 153 

given innovation is not dangerous, before proceeding to 
say confidently that the time has come when it may 
be made." Very true, but I am now shifting my own 
ground, and trying to fasten on my questioner a positive 
assertion which he has never made. I have quite ignored 
the third alternative that lies between 'saying confidently 
that the time has come ' and my own equally confident 
original assertion that such time has not yet arrived; 
namely, the alternative of holding my tongue, or at least 
of softening assertion into mere suggestion and asking 
modestly to hear the possible objections. If my opponent 
understands the doctrine of the burden of proof, he 
naturally proceeds to point out my mistake. We need 
not develop this particular argument any further, since 
enough has been shown to illustrate the point imme- 
diately before us. Whatever reasons I may produce, so 
long as difficulties in seeing their cogency are genuinely 
felt, it is clearly my concern to remove them if I can. 

Secondly, it seems undeniable that even the most 
cautious sceptic cannot escape a certain responsibility. 
The burden of proof must rest on him who asserts that 
an assertion is doubtful, just as much as on him who 
asserts it true or untrue. But two very different mean- 
ings may be distinguished, in calling an assertion 
doubtful, — the one, that I (the objector) feel a doubt; 
the other, that you (the assertor) ought to feel one. If 
I merely intend the former of these two meanings, my 
responsibility (which may still be fully admitted) applies 
not at all to the point at issue, but to a matter of side- 



154 FALLACIES. [Part II. 

interest, — the question whether I am, or am not, honest 
in making the demand. It is conceivable that I shall 
not take any pains at all to avoid the imputation of 
quibbling. The sceptic may in general be more easily 
content to leave the other side alone. We are seldom as 
anxious to prove our ignorance or obtuseness as to prove 
our knowledge or insight, and hence the sceptic may 
cheerfully neglect such burden as falls on him. And, in 
any case, the course he chooses to take in this matter 
does not affect the point at issue between the parties. 

Lastly, it follows that even he who asserts the most 
widely accepted doctrine cannot escape the ' burden ' of 
supporting it by reasons. The burden of proof rests, for 
example, on those who maintain the theory of gravitation 
or of the rotundity of the earth, just as truly as on any 
one who should set up for his thesis the denial of either : 
the difference is that in asserting such truths as these the 
burden is apt to pass unnoticed, from the fact that the 
evidence is strong enough to shift it easily, while in 
denying them the burden might really be felt as a 
serious weight. And this leads us to speak of the chief 
practical difficulty in the matter, — the point where 
Practice demands that inquiry shall be stifled. 

Whately's doctrine of the burden of proof* was 
brought forward, as his readers will remember, partly for 
the purpose of annihilating Infidelity by a short and 
easy method : but it is none the less worth considering 
in itself, since the confusion into which he fell is a very 

* Rhetoric : Part i. chap. iii. § 2. 



Chap. III.] THE BURDEN OF PROOF. 155 

excusable one, though probably not often effective against 
the more modern kind of Infidel. " There is a Presump- 
tion " he writes " in favour of every existing institution " 
. . . "Christianity exists; and those who deny the 
divine origin attributed to it are bound to show some 
reason for assigning to it a human origin." Of course, 
there is " a presumption in favour of any existing institu- 
tion." Since it already exists, any one wishing to abolish 
or alter it must, of course, in the first place make an 
assertion to that effect, and also produce his reasons, — 
or else nothing will probably be done. But a pre- 
sumption of this kind is a very different thing from a 
presumption that an assertion made by an existing 
institution is true. Various forms of Paganism exist; 
are we therefore to believe Avithout inquiry whatever 
their followers may choose to assert about them ? No 
doubt this verbal ambiguity was complicated also with 
another confusion, — that between denying and question- 
ing the divine origin of the institution : the Archbishop 
very naturally failed to put himself exactly in the position 
of a real unbeliever, and was considering only the case 
of one who should set out to prove to a believer that 
his belief was misplaced. In such a case certainly the 
burden would in the first place lie on the infidel, as 
being the person making the assertion. But it is surely 
not often that infidels are so generous. Or rather, to 
put it more fairly, they have not the same reason to be 
anxious to convert believers as the latter have (ad- 
mittedly) to convert them, — since no infidel pretends to 



156 FALLACIES. [Part II. 

believe that a Christian will miss incalculable benefits on 
account of his Christianity. Hence it is the unbelievers 
who really take the unassertive position, not professing 
to have any valuable information on the points directly 
in question, which information they are eager to impress 
on the other side ; but quietly willing to examine (with 
minds, at least professedly, open and candid) any asser- 
tions brought forward and supported. It is the believer 
whose mind — even on his own showing- — is no longer 
open : he it is who claims to have already weighed all 
the arguments and arrived at a firm decision; who 
claims the possession of valuable information which he 
is burning to impart, — information so valuable that, 
except on the plea of extreme difficulty in producing 
unexploded reasons, it seems almost cruelty on his part 
to be content with bare assertion. Certainly, any one who 
should set up, to a believer, the thesis 'Christianity 
is of purely human origin' must bring forward his 
reasons for that thesis, or else expect the believer to 
remain unshaken : but on the other hand any one who 
sets up, to an unbeliever, the thesis ' Christianity is of 
divine origin ' is in exactly the same position. Professed 
ignorance, however often a mere pretence, and however 
often (when real) a sign of culpable indifference or of 
pitiable want of power, is also the natural and normal 
position of the anxious mind, until anxiety is removed by 
the production of evidence that at least seems sufficient. 

And here it seems in place to notice that the real 
difficulty as to the burden of proof is somewhat deeper 



Chap. III.] THE BURDEN OF PROOF. 157 

and more serious than might be supposed either from 
a bare statement of the fundamental rule, or from a 
rough description of the cautious attitude in one or 
two rather artificial controversies. In Logic altogether 
there is often a danger of treating words as more than 
counters, and so of giving an air of wordiness and 
trickery to the results attained ; and in all this matter 
of the burden of proof the danger in question is perhaps 
especially active. It is not only in disputes and verbal 
arguments that the correct placing of the burden is 
important, but wherever we are called upon to judge 
whether all objections to an assertion have been properly 
taken into account ; as where, for instance, we have to 
decide between accepted theory and awkward fact. The 
difficulty at last resolves itself into that of saying what 
shall constitute 'practically conclusive ' prejudice. 

How far, for example, are we 'bound to explain 
away ' a so-called fact ? If we already have an ap- 
parently well-established theory regarding, say, the 
impossibility of corpses reviving, or of ■ spirits ' holding 
communication with the living, or even if our theory 
goes no further than to deem some given behaviour 
of mind or matter a physical impossibility, what is the 
rational attitude towards a claimed miracle, or ghost- 
story, or mere narration of marvellous fact for which no 
explanation is offered ? 

We need not now, of course, hesitate at any 
purely verbal obstacle. We may say, if we like, that 
the bare notion of a ' miracle ' involves a contradiction 



158 FALLACIES. [Part TL 

in terms ; this merely means that if we were sufficiently 
wise there would be no room for wonder. But that the 
blind should receive their sight in an unexpected manner, 
or that a conjuror's performances should lie beyond our 
powers of explanation, involves no contradiction or im- 
possibility, except on the assumption that we have 
already exhausted all there is to learn When Mr. 
Venn * says that " few men of any really scientific turn 
would readily accept a miracle, even if it appeared to 
happen under their very eyes," what is meant is that, 
though surprised at first, they would either " soon come 
to discard it afterwards, or so explain it away (i.e. bring 
it under known laws) as to evacuate it of all that is 
meant by miraculous." 

The rough and ready doctrine may be called that 
of the existence of ' fair presumptions/ whether left 
indefinite, as in common parlance/!" or — as in law — 

* Logic of Chance, p. 450. 

t And perhaps in Science. Thus Professor Tyndall, in speaking 
(Floating Matter of the Air, p. 305) of the experiments to disprove 
Spontaneous Generation, claims that whereas life in the sealed test- 
tube may always be due to errors of manipulation, the absence of life 
" involves the presumption of correct experiment." The difference 
between scientific ' presumption ' and unscientific is, however, worth 
noting. By this claim it is not meant that a single failure to find life 
in certain conditions is sufficient at once to remove all doubt : the 
patience with which Professor Tyndall's own full investigation was 
conducted bears witness to the contrary. But it is merely claimed that 
where the instances for and against are equal in number, the evidence 
is " not equally balanced," and that " as regards the fruitful flasks 
[a careful inquirer] would . . . repeat the experiment with redoubled 
care and scrutiny, and not by one repetition only, but by many, assure 
himself that he had not fallen into error." 



Chap. III.] THE BURDEN OF PROOF. 159 

defined to some extent by set rules. It amounts, in 
brief, to this, that where there exists a ' fair presumption ' 
in favour of a belief, or where a belief is in harmony 
with prevailing opinion, the assertor is not ' bound ' to 
produce evidence, but that whoever doubts the assertion 
is bound to show cause why it should not be believed. 
The value of this procedure, as a short cut or as a weapon 
agahist mere obstruction, must be apparent at once. A 
Law Court, for example, one of whose unavoidable limi- 
tations seems to be the occasional necessity of sacrificing 
the individual to the average — i.e. of resting content with 
caring not at all about the minima of justice — may derive 
on the whole great advantage from such special rules, at 
any rate as regards speed in getting through its work. 
Thus, a person found in possession of stolen goods soon 
after the theft, is presumed to be the thief, and has to 
prove innocence although he is the accused party. If 
a married woman in this awkward situation proves that 
she stole the goods in the presence of her husband, but 
asserts that he compelled her to steal them, she escapes 
the burden of proving this latter assertion, since the Law 
considers it self-evident* And every rule that dictates 
in general how given facts or admissions shall be con- 
strued, is an example of this procedure. Convenient, how- 
ever, as such a plan may be where there is an authority 
competent to frame the rules, it is obvious that out- 
side certain artificial institutions, existing for some 

* Cf. Stephen. Digest of the Law of Evidence. Articles 95 and 96. 
Cf. also De Morgan : Formal Logic, p. 201. 



160 FALLACIES. [Part IL 

special purposes, no such authority exists. Argument 
in general cannot undertake to be bound by what this 
man or the other, or any body of men, may happen to 
consider a ' fair presumption.' Logic shrinks into mere 
cleverness under the bondage of Rules for Debate, and 
dogma cramps the reasoning powers. If, as Whately 
claimed, those who put forward assertions in harmony 
with ' prevailing opinion ' were to be altogether exempt 
from giving a reason for the faith that is in them, or 
if those who bring forward facts in opposition to pre- 
vailing opinion were to be thereby ruled out of court 
at once, with whom would rest the right of deciding what 
assertions and facts really come within such privilege ? 
Even an Archbishop, it must be acknowledged, might 
fail to catch the precise moment when a struggling truth 
really begins to ' prevail : ' and ordinary folk, who only 
desire to follow the safest leader, have often the greatest 
possible difficulty in deciding which party shall claim 
their allegiance and support. At least it might very 
well happen that any two people should fail to agree 
as to what is the prevailing opinion, — much more, as to 
what it ought to be. Perhaps then we must rely upon 
the submissiveness of our audience ? Such a view comes 
near being an ' Idol of the Cave.' Rather, it should 
perhaps be called an Idol of the Hothouse, — a tender 
plant, that can never thrive long in the open air. 

Common-sense has, of course, a very justifiable liking 
for short cuts wherever practicable. Rough and ready 
rules for interpreting facts have a value certainly, 



Chap. III.] THE BURDEN OF PROOF. 161 

even outside a Court of Justice. But there is all the 
difference between using these as our servants, and 
allowing them to become our masters. So long as they 
are employed confessedly as a mere apparatus for saving 
time at the cost of some exactness, no harm is done : for 
where the thesis is more than usually important we can 
take more than the usual care. But if we suppose that 
whenever a bold assertor takes refuge behind his two- 
thirds majority, the spirit of free inquiry ought at once 
to apologise tamely for having dared to put awkward 
questions or to bring forward awkward facts, we have only 
ourselves to blame for the loss we suffer. The assertor 
who shirks inquiry can always be shown to be shirking, 
by the simple process of putting the question clearly and 
letting others see that it remains unanswered. 

Both the practice of relying on prevailing opinion 
then, and also readiness in accepting subversive facts as 
undeniable, have a double edge, and need a little care 
in using. If Science lays down a theory, or Guess- 
work a doctrine, conflicting facts or probing questions 
may both be awkward. But a question differs, after all, 
from an asserted ' fact ' in one very important particular, 
— it carries no burden itself. A ' fact ' stands in need of 
evidence, whether or no it conflicts with theory: and 
clearly, the firmer the theory the greater the caution 
required in accepting evidence for the conflicting fact. 
We find, no doubt, very often, that the ease (or difficulty; 
with which a ' fact ' is accepted depends more on pre- 
judice against (or for) a given theory than on the presence 



162 FALLACIES. [Part II. 

(or absence) of undeniable support for the fact itself: but 
even where the fact does rest on evidence of its own, 
we should not forget that in judging that evidence 
also there is involved a very large amount of rough 
and ready presumption ; that in all observation there is 
involved a certain amount of inference. To say that the 
supporter of a theory is in any way ' bound to explain 
away' a given supposed fact, may be just as high-handed 
a proceeding as for the theorist to condemn the fact 
unheard. It must be proved to be a fact before it has 
any bearing on the theory; otherwise, it is clearly a 
case of "so much the worse for the facts." There can 
thus be no law laid down which shall settle all disputed 
cases a priori: we can only come back, after all, to 
the one fundamental principle that wherever proof is 
demanded, we must either be prepared with sufficient 
evidence, or prepared to see the hopeful proselyte un- 
convinced. 

Shortly, we may sum up the worst of the difficulties 
surrounding the question as to the burden of proof as 
due partly to the unfortunate ambiguity of the expres- 
sion itself, and partly to an endless source of trouble, — 
the practical need of striking some balance between faith 
and hesitation. The mere ambiguity of the expression 
may be met by remembering that the ' must ' of the rule 
is only sanctioned by the assertor's eagerness to convince 
his audience ; and that to ' assert ' must therefore be 
defined to exclude that milder type of assertion where 
we either state an opinion as a fact in our mental history, 



Chap. III.j THE BURDEN OF PROOF. 163 

or tentatively and with a view to learning what the 
objections to it really are. 

In Logic, then, when we speak of the burden of proof, 
we are not speaking of some artificial law, — some merely 
legal, or perhaps Parliamentary rule, — with artificial 
penalties attached to it. No doubt much that has been 
written, even in logical works, has been written with 
some such view. For centuries after Aristotle's time, 
argument appears to have been regarded as a kind of 
intellectual game, in which each player might try to 
obtain what advantage he could, so long only as he 
obeyed the rules laid down. The microscopic ingenuity 
with which the Schoolmen carried on the elaboration of 
these rules was well worthy of a better object. But here, 
at any rate, we are free from any such limitations. No 
penalty follows the misplacement of the burden of proof, 
in the strict sense in which we here use the expression, 
except the natural consequence that the assertion remains 
untested, and the audience therefore (if inquiring) un- 
convinced. To lay the burden on another, therefore, 
is not to demand Proof at the point of the sword, but 
rather to request it as a favour. There is no ' obligation ' 
on any one to prove an assertion, — other than any wish 
he may feel to set an inquiring mind at rest, or to avoid 
the imputation of empty boasting. It is a natural law 
alone with which we are here concerned, — the law that 
an unsupported assertion may, for all that appears, be 
either true or false. And a corollary is that the more 
intelligent the audience the less easy will it be to pass 



164s FALLACIES. [Part II. 

off upon them a bare assertion under the pretence that 
they are in any way ' bound ' to disprove it or explain 
it away. 

And, as regards the practical need of recognising fair 
presumptions, the best key seems to be to keep quite 
clear the fine distinction between two really different 
doctrines ; one, the firm foundation of all the cogency 
that Proof can ever attain, and the other the tottering 
shelter for boastfulness that fears to be found out. The 
former may be described as the doctrine that before we 
can safely accept a given theory we are bound to discard 
all possible rival ones : the latter the doctrine that before 
we can presume to decline to accept a given theory, we 
are bound to provide an efficient substitute. Nakedly 
stated like this, perhaps, their difference is easy enough 
to see, but there are aspects (or uses to which they may 
be put) under which they become rather more difficult to 
keep distinct. Thus, for example, a theory occurs to us 
as satisfactory, and instead of actively trying to find out 
all that can be said against it, or what rival theories are 
possible, we entitle it a ( provisional theory/ or a ' work- 
ing hypothesis,' and then proceed at once to dismiss all 
doubts from our mind. I am not, of course, saying that 
this provisional contentment is always to be avoided, — 
only that there is more of it in circulation than would, 
perhaps, be the case if our notions of the burden of proof 
were kept quite clear. The inclination to believe without 
inquiry has long ago become a confirmed habit of the 
human race; dating, no doubt, from the times when 



Chap. HI.] THE BURDEN OF PROOF. 165 

sheer necessity — poverty of knowledge — led us to invent 
our facts : while the use of provisional theories as such, 
i.e. with full recognition of their imperfections, seems to 
be an art which, with all our good intentions, we are 
only slowly learning. 

Further, since where no Reason is given the Thesis 
may be either true or false, a second corollary is, as already 
noted, that the absence of a reason given is no conclusive 
condemnation of the assertion made. Whether it should 
even raise a presumption of weakness depends, of course, 
on circumstances. It would not do so, for example, 
where the assertor, without any motive for untruth, is 
merely relating unmistakable facts within his own ex- 
perience, — as that he came down by the Midland Rail- 
way, or that he usually buys his books at a certain shop. 
As a broad rule, in fact, we might say that the need for 
proof depends on three classes of circumstances, — the 
likelihood of mistake, the likelihood of falsification, and 
the importance of the assertion made. Where all three 
of these are at a minimum, the need for proof is at a 
minimum too : where any one of these rises into pro- 
minence, the demand for proof begins. Thus the asser- 
tions (1) that I saw a ghost, or, (2) that defendant was 
elsewhere at the time the deed was committed, or, (3) 
that the earth will be baked to a cinder in 1897, would 
be generally felt to stand in need of evidence. Closely 
bound up with the need of Proof is, of course, the pre- 
sumption of weakness which its continued absence is apt 
to raise. That is to say, where the need is strong the 



166 FALLACIES. [Part IL 

call is usually audible ; and deafness is known to be often 
largely voluntary. But so far as appears, no general 
rule can be framed for judging of the strength of such 
presumption in a given case. Even distinct unwilling- 
ness to produce the grounds of belief is an ambiguous 
sign, — much more so is the mere absence of evidence, 
however strong the call for Proof. Unquestioning faith, 
for example, — the failure to see any necessity for ex- 
amining the grounds — is often a cause of unsupported 
assertion. So is the simple desire to avoid trouble. So 
is distrust of our audience. So again, as already noticed, 
are the mere number and extent of the reasons, and our 
fear of failing to do them justice. Insecure faith — the 
fear of losing the belief if strict inquiry should be made — 
is only one cause among many : nor, even if it were the 
sole explanation of such unwillingness, would the sign be 
beyond dispute. For misplaced timidity in our beliefs 
is not altogether unknown. 

Much the same applies to the case where the assertor 
does produce evidence, time after time — either old argu- 
ments or new ones — and yet every time such evidence is 
found, by the best tests obtainable, to be insufficient. 
The practical difficulty is that of saying where our rooted 
distrust shall begin. The failure of argument, however 
long continued, never indeed amounts to conclusive dis- 
proof; since either the real difficulty in producing the 
sufficient grounds, or the assertor 's want of skill, may be 
to blame. But it can hardly be denied that the pre- 
sumption does in certain cases become very strong 



Chap. III.] THE BURDEN OF PROOF. 167 

indeed, — quite sufficiently so for many rough practical 
purposes. Since, however, there does not yet appear to 
be any means of generalising the cases satisfactorily, it 
seems best only to notice this as a standing difficulty in 
the complete practical theory of Proof, at present beyond 
the reach of anything more definite than what may be 
called a kind of logical tact. It is, however, a side issue, 
and does not affect the 'burden of proof itself. 

It is quite possible, therefore, to be over-pedantic or 
vexatiously unpractical, in demanding Proof, just as in 
demanding explanation of the meaning of a term. And 
in this case as in the former the question whether a given 
demand is on the whole conducive to the interests of 
practice may indeed itself be raised and answered, but 
otherwise lies quite outside the scope of our inquiry. 
In strictness any assertion may have its grounds called 
for; and until they are produced and examined, the 
assertion remains untested. Whether practical con- 
venience decides that in certain cases the assertion may 
safely be left in this state, is another matter. We are 
only concerned with those assertions which are already 
erected into theses; i.e. which have, in the opinion 
(mistaken or not) of the audience, sufficient importance 
and doubtfulness to make proof desirable and demanded. 



SECTION II.— NON SEQUITUE. 
CHAPTER IV. 

INTRODUCTORY. 

When a real assertion is made, and reasons of some sort 
given for believing it, such reasons may perhaps be 
inadequate as a guarantee. In a former chapter (p. 102) 
it was noticed that all the dangers in accepting any 
Reason as evidence for any Thesis, may be reduced to 
the two main heads, (1) Failure in formal adequacy, and 
(2) Failure in material truth, of such Reason ; and 
further, that the first of these departments is the only 
one that needs analysis in Logic. Non sequitur is thus 
co-extensive with failure in the formal adequacy of the 
Reason. 

We here reach what may be considered the central 
and most important part of the whole subject, and the 
part which certainly presents by far the greatest 
difficulties. The chief source from which these difficulties 
flow is one whose influence is not confined to Logic, but 
is felt more or less in all departments of knowledge, — 
the need for compromise between the completest possible 



Chap. IV.] INTRODUCTORY. 169 

investigation and a sufficient degree of speed in practice. 
It seems to be inevitable that in applying Logic some 
compromise between these conflicting desiderata should 
be made : all that can be done is to recognise the com- 
promise as such, keeping a jealous guard against un- 
justified encroachments, yielding, of course, where it can 
be seen that the gain is worth the price, but in such 
cases remembering always that a certain risk is being 
run. 

To speak less generally, the main difficulty against 
which any methods for the accurate detection of Fallacy 
have to contend is the convenient practice of employing 
guesswork. In many cases it is possible to see at a 
glance, with quite sufficient accuracy, what the cause of 
the fallacy has been ; and it is then, perhaps rightly, felt 
as a* waste of time to set about the search in any lengthy 
painstaking fashion. When, for instance, such an argu- 
ment is met with as that " we ought to be guided by the 
decisions of our ancestors, for old age is wiser than 
youth," even the most cautious person can hardly help 
feeling a high degree of security in guessing that the 
operative cause has been some misinterpretation of the 
meaning of Reason or Thesis or both, whereby the full 
difference between ' ancestors ' and ' persons old in age ' 
has been overlooked. So again where we find it argued 
that ' every effect must have had a cause, since otherwise 
it would not be an effect,' we are, no doubt, justified in 
suspecting some attempt to argue in a circle. So in a 
considerable number of cases Common Sense can lay a 



170 FALLACIES. [Part II. 

finger at once on the cause of the fallacy, and thus go to 
the root of the matter without elaborate inquiry. 

A very little inspection of actual instances, however, 
will show that this is far from being always so easy. 
The causes of Non sequitur are manifold, and in the 
large majority of cases the same false argument may be 
due to one of several ; and these, morever, not necessarily 
acting in isolation, but as a rule two or three combining 
to establish a false belief. A given fallacy may be partly 
due to misinterpretation of language, partly to forge tful- 
ness of logical principles, partly to incomplete analysis of 
facts observed, and so on : the union of causes often makes 
their strength. Whether or no it is these difficulties, 
however indistinctly felt, that have led several writers 
to declare the systematic treatment of fallacies to be 
altogether hopeless, at any rate the facts have been dis- 
tinctly recognised and deplored by others. Whately, for 
instance, writes, " It must often be a matter of doubt, or 
rather of arbitrary choice, not only to which genus each 
kind of fallacy should be referred, but even to which kind 
to refer any one individual fallacy." And he further 
speaks of the "utter impossibility" of framing any 
classification which shall be completely secure from this 
objection. Mill endorses Whately 's opinion, but intro- 
duces into his own list of fallacies one class — those of 
Confusion — under which he says, "almost all fallacies 
might in strictness be brought. ... A fallacy can seldom 
be absolutely referred to any of the other classes." The 
outcome of all which is, that it is very easy to give an 



Chap. IV.] INTRODUCTORY. 171 

actual case of fallacy a wrong name, very difficult (hope- 
less except by means of special knowledge of the circum- 
stances) to be sure that we have named it rightly ; and 
quite impossible to guarantee that even the honest 
fallacious reasoner can be made, in this way, to see his 
error. "We are led then to recognise 'Plurality' (and 
combination) of causes of Non sequitur as a fact, and to 
admit that any attempt to determine what has misled 
another person is open to exactly the same risks and 
difficulties as any other attempt to read our neighbours' 
thoughts or motives. 

What is meant b} T classifying Fallacies or classifying 
anything ? All classes whatever are formed not by 
* Nature ' only, but by ourselves reviewing the facts pre- 
sented there, and wishing to sum them up conveniently 
for purposes of our own. Finding some point of resem- 
blance between A, and B, and C, . . . we give them a 
common name, and thereby erect them into members of 
the class which the name denotes. This is never done 
without a purpose, however dimly conceived ; and such 
purpose is, ultimately, always the comparison of new cases 
with those already known. Just where the possibility of 
identifying instances ceases, the value of any classi- 
fication ceases too. The whole purpose of framing classes 
of fallacy is to enable us to compare any new instance 
of faulty argument with others already known to be 
fallacious, — if possible with the most simple and naked 
example of the class. And if our classes be such that 
the identification of actual instances is "a matter of 



172 FALLACIES. [Part II. 

doubt or rather of arbitrary choice," or, as Mill puts it, 
if men's actual errors will not always or even commonly 
fall into our classes, the preservation of the names 
(unremedied and without full explanation of the limits 
of their use) is likely to lead to a very false sense ot 
security. 

To some readers it may seem unnecessary to raise 
difficulties over the confusion of causes of fallacies with 
1 fallacies ' themselves ; but the fact is, that there are 
few kinds of confusion that are really more difficult to 
avoid. The name 'Fallacy' is commonly used in at 
least four different senses, and before proceeding further 
there may be some use in setting these out, and choosing 
one of them. A ' fallacy ' is used to mean : — 

(1) A piece of false reasoning, in the narrower sense ; 

either an invalid ' immediate inference/ or an 
invalid syllogism ; a supposed equivalent form 
which is not equivalent, or a syllogism that 
breaks one of the rules. 

(2) A piece of false reasoning, in the wider sense ; 

whereby, from true facts, a false conclusion is 
inferred. 

(3) A false belief, whether due to correct reasoning 

from untrue premisses (reasons or sources), or 
to incorrect reasoning from true ones. 

(4) Any mental confusion whatever. 

Now, clearly there is no guesswork required for 
saying what is wrong with a given immediate inference, 
or syllogism, expressed in full. It either is or is not 



Chap. IV.] INTRODUCTORY. 173 

a case of * undistributed middle/ ' illicit process,' and so 
on. But since, in practice, arguments are very rarely so 
expressed, we really run a considerable risk in accusing 
a reasoner of falling into one of these paralogisms. If, 
for example, a person appears to be using an undis- 
tributed middle term (as when he argues that some one 
who ' rushes in where angels fear to tread,' is therefore 
a fool), the error — if error there be — may really be due 
either to his ignorance of syllogistic needs, or to his 
mistakenly confusing the major premiss with its re- 
ciprocal (' all those who rush in, etc., are fools '), or to his 
mistakenly believing the reciprocal true; or, again, to 
some confusion as to the exact meaning of some of the 
separate words employed. And to accuse him of undis- 
tributed middle is, in practice, interpreted as judging 
that it was the first of these four causes to which the 
error may be definitely traced. That which is a fallacy 
in the second, third, or fourth senses above noticed may 
be no fallacy in the first sense ; and similarly that which 
is a fallacy in the third and fourth senses may escape 
being so in the first and second ; and ' mental confusion ' 
is obviously wider than any of the other meanings, 
covering cases which they would allow to pass untouched. 
Hence, the narrower the meaning we give to the word, 
the more liable we become to the danger of undertaking 
to guess at the cause ; and on this account it seems 
better to interpret ' Fallacy ' in the fourth of the above 
senses. 

There is indeed one way in which the old names, 



174 FALLACIES. TPabt II. 

or many of them, may be preserved with real advantage : 
and that is, not by simply deploring the difficulty of 
identification and then thinking no more about the 
matter, but by trying to understand clearly the causes 
of it. So far as we can obtain the law of the difficulty, 
we are in a fair way towards being able to judge in the 
given case whether and how far identification is possible. 
It is therefore on this account that I would draw 
attention to the risk of failure that is always run, for 
the sake of speed, in attempting to find at once the 
source of a given fallacy. However valuable such a 
practice may be for saving time, and however justified 
in certain cases, we must admit with Mill and Whately 
that there are many other cases where it necessarily 
fails. The remedy seems to lie, first in recognising 
clearly and consistently this possibility of failure, 
secondly in trying to improve our process of guesswork, 
and lastly in providing some surer if more lengthy 
method to fall back upon in doubtful or disputed cases, 
— wherever the matter is more important than the time. 
Such a method Logic really furnishes, — that of the 
Reduction to absurdity, * or, as it is more popularly called, 
1 pushing the argument home,' a method not by any means 
infallible, but free at least from the danger just referred 
to. Although Language remains faulty and treacherous, 

* This is, however, to be distinguished from the process so-called by 
Euclid, which corresponds to the ancient " ductio per contradictor 'iam 
propositionem sive per impossibile," by which the moods Baroko and 
Bokardo were to be justified. See Aristotle : Top. viii. 14. See also 
p. 353 of this book. 



Chap. IV.] INTRODUCTORY. 175 

and our knowledge of Nature incomplete, yet if this 
method be fairly and cautiously applied we thus avoid 
at least the too common error of dogmatically misreading 
the mental processes of other people. 

This, then, will be the plan adopted; and having 
already recognised the fact that to guess at the source 
of fallacy necessarily exposes us to a certain risk of 
failure, the next point is to inquire what can be done 
to improve the methods of guesswork. 



CHAPTER V. 

THE EMPLOYMENT OF GUESSWORK. 

I. General and Special Sources of Fallacy. 

For the purpose of attempting to detect Fallacy 
off-hand, it is clear that some classification of fallacies 
is in the first place required : we must be able to give 
the detected fallacy a name. And the most obvious and 
useful principle of classification appears to be the 
attempt to distinguish (1) the main sources of danger 
to argument in general, and (2) the special dangers 
to which special forms of argument are chiefly liable. 
Some such principle, not perhaps always intentionally 
followed however, seems in fact to lie at the root of most 
of the distinctions which have been made by logicians, 
and equally of those which have won a permanent 
place in popular usage. Thus the great distinction 
made by Aristotle, between fallacies in dictione and 
extra dictionem, calls attention to one large general 
source of Fallacy, — the snares of language ; while inside 
the second main class the varieties are partly common 
to, all kinds of argument,— as the Fallacia accidentis 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 177 

(interpreted widely), the Ignoratio elenchi, and the 
Petitio principii, — partly special to special arguments, 
as the Fallacia consequents, the Non causa pro causa, 
and the Fallacia plurium interrogationum. So again 
Mill's division into a priori fallacies and those of 'in- 
ference/ aims apparently at marking off in the first 
place a large source of error common to all forms of 
argument, while under the second head the same function 
is performed again by the class called ' fallacies of con- 
fusion/ the remainder of the second class being divided 
according to the special forms of Inference, namely 
Induction and Deduction. And when we look at the 
names of fallacies which are widely recognised in popular 
usage, this principle of classification is equally noticeable, 
' verbal ambiguity/ ' missing the point/ and ' begging the 
question/ having come respectively from 'in dictione,' 
'Ignoratio elenchi' and 'Petitio principii; and such 
names as ' false analogy/ ' over-generalisation/ ' over- 
looking alternatives/ etc., referring more directly to 
failures in special kinds of argument. 

I propose then to make some use of this principle 
of classification. In face of the difficulties to be en- 
countered, a certain aid towards satisfactory guesswork 
may perhaps be given by examining broadly both the 
chief snares common to argument in general, and also 
those characteristic of the special forms or types of argu- 
ment. And the discussion of both will, I hope, be of 
service towards appreciating the value and meaning of 
the method for reducing to absurdity. 



173 FALLACIES. [Part IL 



II. A List of General Objections to any Argument. 

Probably if any one already accustomed to the practice 
of detecting Fallacies, but yet possessing a mind un- 
burdened with the more abstruse logical technicalities, 
were asked to classify all possible objections to arguments 
in general, the division made would be somewhat as 
follows : — 

1. That the Reason given (or the objection) is beside 
the point. 

2. That the Reason given begs the question. 

3. That some important factor has been overlooked or 
forgotten. 

4. That if the argument be cogent, some absurdity 
(or at least untruth) must also be believed. 

At any rate such a classification does not err on the 
side of too great depth or intricacy. Can it be made 
useful for our present purpose ? 

A note must be carefully registered, in the first place, 
that this division, however obvious at first sight, is 
purely one of convenience, not otherwise defensible. In 
strictness these four, if not quite alternative attacks, 
each equally capable of being made against any unsound 
argument, are at least to a very great extent overlapping. 
It will be seen that the first of these objections corre- 
sponds roughly to the charge technically known as Igno- 
ratio elenchi ; the second to Petitio principii ; the third 
and fourth having received no technical names. But so 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 179 

long ago as Aristotle's time it has been pointed out * that 
every case of Non sequitur may in one sense be viewed as 
Ignoratio elenchi; while it is quite clear that the first 
and second of the above heads are, strictly speaking, 
cases of 'Untruth implied.' If the Reason is beside 
the point, or if the sufficiency of the Reason itself 
depends on the Thesis being true, it is clear that the 
Thesis cannot really depend upon the Reason in the 
manner implied in every argument. As regards Petitio 
principii it would, no doubt, be considered rather a 
straining of language, were we to claim that the other 
heads might be brought under it : and yet, in this rather 
far-fetched sense the name Petitio principii is some- 
times employed, — at least in cases where the point is 
missed and in those in which some palpable absurdity 
is implied. For when we give as valid a reason which 
is beside the actual point at issue, we beg (not indeed the 
expressed original question, but) a question then perhaps 
for the first time seen to be remotely involved in it and 
essential to its establishment ; namely, that of the con- 
nexion between the Thesis which is, and that which ought 
to be guaranteed. This may be seen, for example, in the 
case where metaphor or analogy is employed in argument : 
to the assertion that the growing size of London bodes 
evil to England because London is the heart of England, 
and a swollen heart is a sign of disease, it is clearly 
optional whether we object that "R is beside the point, 
because the analogy does not in fact apply" or that " R 

* Soph. El. vi. 



180 FALLACIES. [Part II. 

begs the question how far the analogy holds good, which 
is the real turning-point of the argument;" or, again, 
that R and T together imply the absurdity (or untruth) of 
supposing what is in fact a mere metaphor to bear literal 
interpretation. In all three cases the objection is funda- 
mentally the same, and our adoption of one form or 
another depends solely on rhetorical considerations. 
Again, where a Reason is given which, taken together 
with the Thesis, leads to absurdity or untruth, we some- 
times hear the objection brought that such Reason begs 
the question by assuming the fact on which the question 
is plainly seen to turn. As De Morgan says {Formal 
Logic, 255), though he strongly objects to the nomencla- 
ture — "It is the habit of many to treat an advanced 
proposition as a begging of the question the moment they 
see that if established it would establish the question." 
R is accused of covertly assuming the truth of some highly 
doubtful proposition which is plainly required to establish 
T. So again it is open to us to view any case of palpable 
question-begging as 'beside the point,' inasmuch as it 
provides no real evidence in support of the point actually 
in question. If for the Thesis ' War is unjustifiable ' the 
Reason be given ' We ought not to do evil that good may 
come/ it is quite optional to object, either that ' this begs 
the question whether war is, on the whole, an evil/ or that 
' the maxim is an excellent one in itself, but beside the 
point in the present case, since war is not necessarily a 
doing of evil/ * And lastly it does not need any lengthy 

* Readers who have been interested in the formerly disputed question 



Chap. V.] THE EMPLOYMENT OP GUESSWORK. 181 

exposition to show that in all cases where Fallacy has 
crept into an argument, some relevant fact, whether as to , 
things or as to the meaning of names, has been over- 
looked. " We might, perhaps," says Mr. Sully,* " charac- 
terize all illusion as partial view," and elsewhere he 
identifies illusion, at bottom, with fallacious inference. 

In spite of such difficulties, however, this fourfold 
division may be put to considerable use in guessing 
at the seat of Fallacy. But it will need some special 

whether or no the Syllogism itself is a Petitio principii, "will easily see 
the connexion of what has just been said, with that ancient difficulty. 
Every Syllogism runs a risk of being in fact a Petitio principii ; it is 
so unless the argument employing it either appeals to admissions already 
made (thus becoming a legitimate argumentum ad hominem), or else only 
aims at forcing into explicitness a principle, or an application of a 
principle, on which the point at issue turns, — in order that the material 
truth, as yet supposed capable of disbelief, of such principle or appli- 
cation may be now inquired into. If I argue that A is B because A is 
C (or because C is B), the Syllogism employed is, of course — C is B: 
A is C : .*. A is B. In using this Syllogism I may be either appealing to 
a former admission that C is B (or that A is C), or I may wish now to 
obtain that admission, and then the further consequence that my thesis 
is true; and lastly I may either try, consciously or unconsciously, 
to hide, or may openly confess, this wish. Supposing the Reason itself 
true, the whole question of the truth of the Thesis turns upon the truth 
of such further assertion implied by Reason and Thesis together, and 
to ' assume ' the truth of such further assertion is, no doubt, to ' assume ' 
that upon which the question really turns. But there are two kinds of 
assumption — underhand (or unconscious), and open, — and it is only the 
former which can do harm. A Syllogism rightly employed is just as much, 
and no more, an assumption of the point in question as every express 
assertion is. If I assert that A is B, I ' calmly assume ' that such assertion 
is true ; but I do so in a manner which, if my assumption is not sup- 
ported by an appeal to valid reasons, exposes me at once to the necessary 
hostile criticism. If the view here taken of the burden of proof be a 
correct one, it is only covert assumptions which are illegitimate. 
* Illusions, 2nd ed. p. 336. 



182 FALLACIES. [Part II. 

care in keeping the classes distinct. We shall have to 
limit the meaning of some of the names, in a way which 
their etymology at least would hardly warrant. 



III. The Objection Ignoratio Elencrl 

First, it should be noticed that the common application 
of the terms Ignoratio elenchi and Petitio principii 
is rather uncertain. As regards the former, we have 
already seen that in one sense it may be stretched to 
cover nearly every possible fallacy, while in another sense 
it is often narrowed to misinterpretation of the meaning 
of the Thesis. A third sense, rather wider than this 
last, is simply the objection that ouing to some con- 
fusion or other as to meaning, the Reason is accepted as 
a guarantee for the Thesis, when in fact either this actual 
Reason at most guarantees some other proposition merely 
resembling the Thesis and mistaken for it, or when some 
other proposition merely resembling R guarantees this 
actual Thesis. When the charge 'R beside the point' 
is brought, in the sense here referred to, what is meant 
is that owing to some misunderstanding, ivhether of B 
or of T, the former is unduly accepted as a guarantee 
for the latter. To use an expression of Mr. Milnes' — 
" The journey has been safely performed, only we have 
got into the wrong train." 

If we accept this meaning, the next thing is to dis- 
tinguish carefully two cases of misunderstanding; first 
where, without any opponent as yet in existence, an 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 183 

assertor brings forward, in support of his Thesis, some 
Reason which, though really valid for some other (similar) 
Thesis, is strictly irrelevant to the present purpose ; and, 
secondly, where the misunderstanding takes the form of 
an objection by an opponent, to an assertion made, or 
an argument employed, by ourselves. It is in the former 
of these two cases that the chief practical difficulty is to be 
found, but in both cases the difficulty is considerable. 

In no department of logical practice, perhaps, is the 
danger of undue dogmatism so great as in that of deciding 
whether misinterpretation has really taken place. This 
is, in fact, the chief point at which the functions of Logic 
are apt to be confused with those of Grammar. Since in 
any advanced language there is much substantial agree- 
ment both as to the meaning of names and of forms of 
speech, and since in such languages Grammar is always 
at hand to confirm and to generalise this agreement as 
far as possible, there springs up easily the supposition 
that meaning resides solely in the words and their 
arrangement, that a printed sentence bears its full inter- 
pretation on its face, which has only to be deciphered 
and the thing is done. But, as a fact, interpretation is 
far from being so simple a matter : the same meaning 
may be expressed in many different forms, and the same 
word or set of words may carry many different shades 
of meaning. If any doubt be felt on this head, let the 
reader take any collection of ordinary examples of pro- 
position, e.g. those in chaps, iii. and iv. of Jevons' 
Studies in Deductive Logic (and these, be it remem- 



184 FALLACIES. [Past IL 

bered, are always artificially straightforward), and ask 
himself in how many of the four traditional forms 
(A, E, I, and O), each will bear interpreting. Still more 
uncertain is the meaning of the separate names em- 
ployed. A few there are, as already noted, the sense 
of which is, practically, fixed ; but these are com- 
paratively few. Not only does the meaning of most 
words in common use undergo a constant gradual change 
as time goes on, but at the same period it varies greatly 
according to the varying knowledge, or even the passing 
emotions, and physical states, of the speaker ; and much 
of what every one ' knows ' he is liable to forget. All 
names which have gathered round them a cluster of 
inveterate associations (and what names have not ?), 
depend for a large part of their essential meaning on the 
past experience, and present mental states and habits, of 
the person using or hearing them. Many words bore a 
different sense to ourselves as children from that which 
they bring to us later in life : though the old names and 
phrases may remain, their meanings grow and alter widely. 
So again, a slight difference in the context, or even in 
less obviously connected circumstances, will often make 
a difference of meaning amounting to the actual reverse 
of that conveyed by the same words at another time : 
witness the possibility of " damning with faint praise," 
or the wrath of authors whose sentences have been 
criticised apart from their surrounding explanations. 
We need not search further for illustrations of so trite a 
fact. The purpose of these remarks is merely to bring 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 185 

to mind the many-sided difficulties attending all attempts 
at finding the exact meaning of an assertion. 

To all this it may, however, be answered that, just as 
in deciding whether a proposition is real or not, so in 
deciding the total question of its meaning, the only 
feasible plan, where doubt exists, is to put questions 
until such doubt is removed. It is here, in fact, that the 
practical value of the third ' Law of Thought ' — that of 
Excluded Middle — comes into operation. That Law, 
regarded as a statement of fact, is of course the barest 
truism, — A is either B or not-B : everything is either 
something, or something else. But its value, in this 
connexion, springs from the fact that, having postulated 
this undeniable truth, we gain the right * to require from 
a speaker the answer Yes or No to any intelligible 
question t put about the meaning of a name or other 
form of speech. " When you say that Solomon was 
wise, do you mean wise according to our present standard, 
or some other ? " " When you say that familiarity breeds 
contempt, do you mean that in every case the maxim 



* It is very difficult to avoid using expressions which, strictly inter- 
preted, may seem to refer to some set of artificial rules for debate. It 
is, however, possible, I hope, to keep these convenient expressions, and 
yet straiu all such meaning out of them ; using them only for brevity. 
Strictly, of course, we have no ' right to require ' any answer at all : 
what is meant is only that if no answer is forthcoming, the argument 
falls through, since either the Thesis or the Reason remains ' unreal ' to 
us who ask the question. 

t It should be noticed that if A sometimes means B, and sometimes 
not, the question, "Do you mean A or not ?" becomes no longer in. 
telligible. 



186 FALLACIES. [Pabt II. 

holds true ? n " When you say that some Irish are indus- 
trious, do you mean that the majority are idle ? " When 
an hon. member said that the House of Commons is 
' largely composed of English gentlemen/ did he mean to 
imply that it is not entirely so composed ? There is no 
limit to the possible varieties of question that might be 
put, and wherever the question itself is intelligible, only 
the two answers — Yes or No — are possible, and one or 
the other must be true. Where doubt arises as to 
meaning, therefore, we have this method at hand for 
removing it. 

But the chief source of misinterpretation is the fact 
that such doubt does not arise as freely as could be 
desired. We do not habitually weigh either our own 
assertions or those of other people — life being short, and 
occupations various,— 7-but are content to throw our words 
out somewhere near the mark, and to seize the gist of 
what is said ; glad if we escape the grosser kinds of in- 
accuracy. Yery likely there are excellent reasons for this 
practice, but it has its dangers also ; and it is about the 
dangers only that we are here inquiring. Apart from 
the plan of systematic questioning, can anything be done 
to avoid misinterpretation ? 

Much may be done, no doubt, but not in the shape of 
a few plain rules. To deal with the pitfalls of language 
at all fully, at least a separate volume would be required. 
In one sense, indeed, the subject is inexhaustible. No 
one can pretend to be perfectly safe from all danger of 
misinterpreting language until he can claim a complete 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 187 

knowledge of all nameable things, and also entire freedom 
from all effects of our ancestors' mistakes in naming ; 
and, so far as this goal remains at present unattained, so 
far there exists a source of misinterpretation against 
which nothing can securely guard. It is true, no doubt, 
that there are many errors in interpretation which 
spring, at least directly, not from imperfect acquaint- 
ance with the things that bear the names, but from 
ignorance of the principles of naming, classifying, and 
defining, from too careless employment of language, or 
from too ready subservience to its tyranny. But the 
task of completely remedying even these defects is a 
somewhat more extensive one than can be here at- 
tempted, except by means of occasional and indirect 
suggestions. 

It is obvious, further, that if there is to be an abso- 
lutely clear mutual understanding between speaker and 
audience as to the meaning of every separate word em- 
ployed, and also of the assertion as a whole, a larger part 
of every speaker's life would be occupied in the process 
of defining, or explaining his statements, than could well 
be spared from his other occupations ; and that, long 
before the meaning of most assertions could be settled, 
their value as practical information w r ould have passed 
away. Accordingly, the point of first importance for 
practice is to know on w T hat principles the compromise 
had better be conducted ; when once there is seen to be 
need of inquiry into the special meaning given to some 
word or phrase, the process of inquiry is simple enough, 



188 FALLACIES. [Part IT. 

and has been already sufficiently indicated. To a de- 
finite question a definite answer may be, with reason, 
demanded. 

Where there are already two opponents, though Igno- 
ratio elenchi is unfortunately common enough, it is far 
less dangerous than in the other case. As a rule, when 
we are met by opposition we are ready enough to 
discover any misunderstanding of our views. The grosser 
cases, at least, therefore, would present no difficulty : it 
will be sufficient to call to mind a few of the leading 
varieties. Thus, mildly denying that a certain thing is 
absolutely all-important, we are met by arguments to 
show that it he,s some use : boldly pointing out that 
something else is altogether valueless, we are met by the 
answer that we ' can't expect perfection : ' asserting that 
some doctrine lacks arguments to prove its truth, we are 
referred to excellent reasons for believing in its utility : 
endeavouring to trace the manner in which some highly 
developed growth (e.g. conscience) originated, we are 
supposed to be refuted by a mere description of its 
present nature : disputing an argument, or an instance, 
we are supposed flatly to deny the theory in support 
of which these were brought forward : making some 
merely tentative suggestion we are asked for definite 
proofs. The varieties are endless, and the reader's ex- 
perience will easily supply him with a longer list of 
instances than we need here set out. 

But the real importance attaching to this kind of 
Ignoratio elenchi begins when we reach the finer shades 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 189 

of it. There is no doubt that the most frequent cause 
both of real misunderstanding and also of interpretation 
which is only too penetrating, is the attempt to read 
between the lines of what is said. Time being short, it 
seems to be generally recognised that some ellipsis in 
expression may as a rule be expected. It saves time and 
trouble in many cases to go behind the actual words, 
answering not what they strictly say, but what the 
objector supposes they really intend to insinuate. There 
are familiar euphemisms, for instance, whose ironical 
meaning is hallowed by custom ; and there are ways of 
saying much by saying little, — and vice versa. 

But probably the most dangerous of all the sources of 
misunderstanding, is the gradual change that unavoidably 
takes place in the accepted meaning of words, so that 
both old and new meanings are, for a time at least, left 
existing side by side. The most marked examples of this 
are perhaps those due to the influence wrought on lan- 
guage by Science, or the deepening of knowledge, on the 
one hand, and by the allegorical or superficial spirit on 
the other ; very many words possess in this way no less 
than three broadly marked meanings, — the scientific (or 
technical), the popular, and the poetical. The various 
meanings in which the familiar word ' Law ' is used, will 
perhaps sufficiently illustrate what is here intended. Or 
again, through what is loosely called mere lapse of time, 
the meaning of a word may wholly alter ; as the word 
* Sophist/ originally from aotpog, has now come to mean 
a quibbler. A public instance of Ignoratio elenehi due 



190 FALLACIES. [Part II. 

to this latter cause, was presented in a recent trial.* " It 
was complained," said counsel, " he had written ' I never 
expected to hear a coxcomb ask two hundred guineas for 
flinging a pot of paint in the public's face,' but .... 
what is a ' coxcomb ' ? / have looked out for the word and 
find that it comes from the old idea of the licensed 
jester, who wore a cap and bells with a cock's comb in it. 
If that is the true definition, Mr. Whistler should not 
complain." So in, perhaps, the majority of cases where 
Etymology is relied upon by an afterthought as giving 
the ' true ' meaning of a word at the present day, there 
is involved some attempt to use the word in one meaning 
and to defend it in the other, f 

We have already had occasion to notice George Eliot's 
reference to " those undeniable general propositions which 
are usually intended to convey a meaning very far from 
undeniable," and it is not only general propositions but 
general names also that are used largely in this manner. 
The meaning of any name consisting, as it does, of very 
many particular facts regarding the objects named, it 
becomes easy on occasion to forget conveniently some of 
these facts while defending our use of the word, although 
we were far from forgetting them in the meaning really 

* Wliistler v. Buskin. 

t Of. Geo. Bentham, Outline of a New System of Logic. " Where 
correct information, and consequently perspicuity in language is the 
object, the greatest attention should be paid to employ, in preference to 
others, such figures as have by long use lost, as it were, their original 
sense." Of. also H. Spencer, Psychology, vol. i. p. 97. " The best words 
are those from which long use has worn away all, or nearly all, traces 
of their origin." 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 191 

intended to be conveyed. The gathered associations, for 
instance, which words take on, and which they are sure 
to convey when used, can be very easily left out of sight 
while defending our use of them. This is especially 
insidious in the case where the meaning of the word used 
is relative to some standard, and where truth or false- 
hood depends upon the standard taken. As marked 
instances may be mentioned 'good' and 'bad,' 'great' 
and 'small,' ' hot ' and ' cold,' and all names which con- 
fessedly indicate points variably selected on a scale. In 
its finer shades the danger is almost ineradicable, since 
the standard employed by different people in judging 
is apt to vary with their personal peculiarities, tem- 
porary or habitual, and past experience ; so that where 
no thermometer can be appealed to it becomes exceed- 
ingly difficult to fix any objective standard at alL Even 
if we understand our intimate friends, it is notoriously 
difficult to make full allowance for difference of standard 
in the case of all our casual acquaintances. 

It is easy, however, in this manner to enumerate a 
few of the leading ways in which assertions may be mis- 
understood, and even to write a loose and general homily 
upon human liability to error in this respect. But there 
seems to me very little practical value in so doing. The 
practical question would be, — What is it incumbent on us 
to do, for the purpose of detecting, and so avoiding, 
misinterpretation? And to answer this with any real 
completeness would lead us further afield than we can 
here afford to go. 



192 FALLACIES. [Part II. 

But as regards the first of the two kinds of misunder- 
standing, it may perhaps be suggested as a broad general 
rule that inquiry into meaning, for the purpose of raising 
the objection that B, is beside the point, is only advisable 
where the person inquiring has himself a definite view, 
if not of all the possible ambiguities involved, at least of 
the fact that some given ambiguity is probable. It is 
true that in this way much false argument would pass 
unnoticed, but the only alternative seems to be a loss of 
more time than the results would probably justify. If 
in every case where an assertion is made and grounded, 
it were to become at once incumbent on us simply to 
assume, until the contrary was shown, that some irrele- 
vance was present between II and T, it is clear that the 
waste of time would be on the whole enormous. 
Although Ignoratio elenchi may be the commonest of 
all fallacies, and although, perhaps, some slight shade 
of uncertainty as to our meaning is present in nearly all 
assertions actually made, nothing would, I think, be 
practically gained by treating intelligent assertion as the 
exception, verbal confusion as the rule. There should be 
something to set us on the track of an Ignoratio elenchi; 
we should not be left under the necessity of inquiring 
for it at large. 

If this be admitted, — and I see no resource but to 
make the admission, — it follows that the power of guard- 
ing against this kind of mental confusion is not one 
which can be given in a few hours or days, by the 
careful study of any dissertation on the subject, however 



Chap. V.] THE EMPLOYMENT OF GUESSWOEK. 193 

searching and complete. It must be rather a growth, 
dependent on the growing power and habit of distinguish- 
ing between the different senses which any given word 
or phrase may bear. It is the power of seeing difference 
that is of prime importance, — difference, in this case, 
between one possible meaning and another. And the 
power of seeing differences cannot be obtained by merely 
recognising its value, though that is no doubt one im- 
portant step towards the attainment of the power. 

As regards the second kind — that which more truly 
corresponds to the literal meaning of Ignoratio elenchi, 
— it may also, I think, be laid down that the assertor 
is, in every case, the arbiter of what he means to say. 
Where, under cross-examination, he contradicts himself, 
or shifts his ground, this can be pointed out, and the 
request can be made that he will abide by one alterna- 
tive or the other. He either means a given thing or he 
does not. There is no middle ground between * Yes ' and 
'No/ 

IV. The Objection Petitio Peincipil 

A similar difficulty exists in fixing the meaning of 
Petitio principii, to that noticed already in the case 
of Ignoratio elenchi. De Morgan observes * that 
"Aristotle hardly ever uses the phrase apxv v aiTtiaOai, 
principium petere : it is To l£ apxvQ? and To lv apxg, 
that which is (ought to come) out of, or is in, the prin- 

* Foi-mal Logic : p. 256. 



191 FALLACIES. [Part II. 

ciple. By the word principium he distinctly means that 
which can be known of itself." ..." Among the earlier 
modern writers, as far as I have seen them, there is some 
diversity in their description of the petitio principii. 
That the principium was meant to be the thing known 
of itself, the apxn of Aristotle, as far as the introduction 
of the word is concerned, seems clear enough. Was it 
not then by a mere corruption that it was frequently 
confounded with the conclusion, the 'quod in principio 
quoesitum fuit ? ' Did not the same inaccuracy, which 
confounds the To ev aoxy °f Aristotle with the apx>i 
itself, govern the change of the word? Most writers 
take the fallacy of the petitio principii as meaning that 
in which the conclusion is deduced either from itself, 
or from something which requires proof more, or at 
least as much, ignotius, ant deque ignotum." And De 
Morgan's own opinion seems to be (ibid. p. 254), that 
" strictly speaking, there is no formal petitio principii 
except when the very proposition to be proved, and not 
a mere synonym of it, is assumed." Nothing, however, 
appears to be really gained by restricting the name to 
so small a compass as this ; and there is no doubt that 
such a restriction would be very much at variance with 
the popular acceptation of the term. Still, some restric- 
tion seems needed, or else, if we define it as 'covert 
assumption ' in general, it is difficult to say where the 
application would really stop. Although, even on so 
wide a view, deductive proof would not be a begging of 
the question, since there the turning-points of the argu- 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 195 

ment are openly appealed to ; yet, on the other hand, we 
should have to say that question-begging in its finer 
shades begins where there is even an unconscious fear 
of allowing Principle and Application to stand their 
trial. 

Question-begging, then, as we shall understand the 
term, never arises except in two cases ; namely, (1) where 
the relevancy, and (2) where the truth of R is already 
called in question, and where in answer to such objection, 
some proposition equivalent to (or including) the original 
T is given in support. Of the first of these cases, an 
example given above (p. 169) may be taken as fairly 
typical, — "Every effect must have a cause (T), since 
otherwise it would not be an effect (R)." We have seen 
that to call in question the relevancy of the Reason is, in 
other words, to ask for the missing premiss required for 
full Demonstration, and here it is plain that this can only 
be the original Thesis itself — " Every effect must have a 
cause." For if it be possible that an ' effect ' should hap- 
pen without a cause, then the special signification which 
the name ' effect ' is employed to bear would be lost, and 
its value as a label would accordingly be spoilt. Hence 
in order to complete the formal cogency of the argument, 
we need the material truth of the Thesis, — which is just 
the point at issue. For the second case we may take as 
a conspicuous example the dialogue given by Whately in 
illustration, — but somewhat altered and shortened : — 

" * Every particle of matter gravitates equally.' [T]. 
♦Why?' 



196 FALLACIES. [Part II. 

' Because those bodies which are heavier always contain more par- 

tides, even if more closely condensed.' [B,]. 

' How do you know that ? ' [i.e. ' I doubt whether R, is true. , ~] 

' Because, all particles of matter gravitating equally, [original TJ 

that mass which is specifically the heavier must needs have the more 

of them in the same space.' " 

It is seldom, of course, in practice that we find Petitio 
principii thus openly relied upon. Actual arguments are 
usually longer, more complex, and less explicit, than 
those which are required for illustration. As Whately 
puts it, "A very long discussion is one of the most 
effectual veils of Fallacy. Sophistry, like poison, is at 
once detected and nauseated when presented to us in a 
concentrated form ; but a Fallacy which when stated 
barely, in a few sentences, would not deceive a child, may 
deceive half the world if diluted in a quarto volume." 
But it is by seeing any fallacy in its nakedness that 
we can best learn its central nature, and hence the need 
of sometimes appealing to examples which are so obvious 
as to be free from serious harm. The real difficulty, for 
practice, always lies in the stripping off disguises, and 
reducing what is said, and urged, to T and It. 

And here, too, when we raise the all-important ques- 
tion as to the means of deciding in practice whether 
question-begging has in fact taken place, we become 
extremely liable to the danger of accusing an opponent 
unjustly ; for the means of escape are numerous. Take 
for instance, the following argument of Mr. Jermyn to 
Felix Holt : " You must permit me to check your use of 
the word 'bribery.' The essence of bribery is that it 
should be legally proved. Unproved bribery does not 



Chap. V.] THE EMPLOYMENT OF GUESSWORK. 197 

exist." Here we may, perhaps, have a very strong 
suspicion that the Thesis is needed to support the 
Reason. The Thesis evidently is " This case <^ (i.e. differs 
from) bribery ; " and the Reason " Bribery — > judicial 
conviction thereof," (the further assertion being 
"This case H — > judicial conviction of bribery.") It 
seems almost quixotic to hesitate to accuse the speaker 
of begging the question, for it is clear that if this 
case is bribery (which is the point at issue) the Reason 
must be untrue, — provided, at least, as Felix Holt 
would certainly have admitted, that no judicial decision 
had yet been given against the case in question. And 
yet, if we accuse Mr. Jermyn of begging the question, 
he has an easy escape. " I mean," he would say, " to 
assert in the plainest language, that it is little short 
of libellous to accuse another person of bribery with- 
out bringing legal proof to support such accusation." 
This may, it is quite evident, have been his real 
intention in the speech. That is, his speech may 
have been an Ignoratio elenchi so far as the question 
bribery or no bribery is concerned. But by treating the 
argument in a less hasty manner, the covert assumption 
may be prevented quite as effectually and without run- 
ning the risk of mistaking the speaker's intention. " Do 
I understand you to assert," we might ask, " that if A 
pays B for his vote, no bribery has been committed, 
unless and until the fact is proved in a court of law ? If 
such a transaction does not in itself deserve the name of 

bribery, what name does it deserve exactly ? It is of 
10 



198 FALLACIES. [Part II. 

such transactions that I wish to speak, whatever their 
name may be." 

So far as question-begging may be due to misinter- 
pretation of the language used, the difficulties are of 
course the same as those briefly noticed in the preceding 
section. But more commonly it is the result of much the 
same state of mind as that which leads to Platitude. We 
have already had occasion to notice the nature of the 
harm done by tautologous propositions and circular ex- 
planations, and since Proof is the counterpart of Explana* 
tion, and every argument merely a complex proposition, 
it is easy to see the fault of circular Proof. If we start 
with the implied supposition that the Thesis is true, it is 
obvious that the more correct the subsequent logical 
process, the more certain shall we be of reaching the 
required result. Such Thesis has therefore had no fair 
trial : its supposed ' proof ' has been a pretence. Essen- 
tially the same, too, is that commonest and most insidious 
of all practices, the employment of what Bentham called 
" question-begging names." If a name properly belongs 
to S, the whole meaning of that name is applicable : but, 
at the same time, if part of the meaning is plainly ap- 
plicable, we are apt to suppose that the name may be 
' properly ' applied. In this way the leap from part to 
whole is easily made, and the assumption hidden.* 

* This form of Petitio principii is of near kindred to False Analogy 
(see p. 265), and also to material untruth of the minor premiss in an 
ordinary deductive argument. The difference is, in fact, like that be- 
tween analogy and metaphor, a gradual difference, depending on the 
degree of explicitness merely. In the deductive argument we rest our 



Chap, V.] THE EMPLOYMENT OF GUESSWORK, 199 

It is not, however, only when we wish to deceive, nor 
even only when we use words carelessly, that this danger 
arises : for the number of words that have gathered no 
associations — especially associations of praise or blame 
— is comparatively small, and with the best intentions 
and the greatest care it is difficult to avoid all taint of 
question-begging. It is through the power of these 
associations to prejudge a question that so much import- 
ance is attached to the exact name given, even by a person 
Who is himself fully capable of using words as counters 
merely : in the absence of a colourless word, and in the 
presence of two words highly tinged with opposite 
colours, he is forced to choose that which will mislead 
the least. " It is said that we have failed in Ireland. 
I do not admit the failure. I admit the success to be in- 
complete." In the same way, the choice between ' reign- 
ing ' and ' governing,' between l sovereign ' and ' suzerain/ 
between ' mob-rule ' and ' popular government,' between 
' liberty ' and ' license,' between ' famous ' and ' notorious/ 
and between endless other pairs of alternatives, may 
often lead to unavoidable unfairness, or at best to a rough 
balance between opposite wrongs. 

The remedy is essentially the same in this case as in 
all other cases of Petitio principii ; and, in a wider 
sense, in all cases of fallacy, — the forcing into daylight 
that which would prefer obscurity. Names in themselves 

case quite openly on the disputable premiss that ' S is M ; ' in the argu- 
ment from analogy we suggest ' S is, as it were, M,' or f practically the 
same as ' M ; while, if we desire to beg the question by means of a 
name, we assume as quietly as possible that the name applies. 



200 FALLACIES. [Part IL 

are harmless so long as their misleading associations can 
be kept away from them, and by putting the point-blank 
question whether or no this or that meaning is intended, 
the assumption, if any, may be compelled to produce its 
credentials, or to confess that these are wanting. More 
than this Logic can never do. A fallacy stopped at one 
moment may always bide its time, and come into opera- 
tion again when the incident has been forgotten and the 
pressure removed: and, as just seen, this is a danger 
which all names that are rich in gathered associations 
especially tend to foster. On this account it is that in 
cases where, as so often in Politics, the determination is 
strong on both sides to take every possible advantage, 
however unfair, there is often practically no better re- 
source, even in the interests of truth and fairness, than 
to meet question-begging with its own weapons, just as 
one false analogy may often be met and destroyed by 
another equal and opposite. In this way, out of two 
wrongs a rough and ready right may be made to emerge. 
But here we certainly step over the line which divides 
Logic from Rhetoric, or the task of detecting and recog- 
nizing Fallacy (or, as an alternative, preventing it for 
the moment) from the wider problem of counteracting its 
operation- 



CHAPTER VI 

THE EMPLOYMENT OF GUESSWORK : CONTINUED. 

I. The Objection 'A Factor overlooked.' 

It is difficult to find any one short name which shall 
fairly describe the third of our four general objections 
to an argument. We have already noticed that in the 
ordinary sense of the words, some important factor has 
been overlooked or forgotten wherever any fallacy — even 
Ignoratio elenchi or Petitio principii — has been com- 
mitted ; so that the name here taken is too vague to be 
really descriptive. And the same difficulty seems to 
attach to any other short name that can be suggested ; 
thus if, for example, we attempt to sum up this third 
objection as the charge of ' superficiality of view,' it 
will be necessary to add that the ' view ' spoken of may 
be either a view of objects, qualities, and events, directly, 
or a view of the meaning of names and propositions. 
For sometimes, in proving, we make use of knowledge 
already formulated, and sometimes we go direct to the 
facts for ourselves : while, according to the special mode 
of argument employed, will be, to some extent, the special 
liability to error. 



202 FALLACIES. [Part II. 

Without, then, spending time in trying to get a per- 
fectly accurate name for the purpose, it becomes necessary 
now to examine, briefly at least, the leading types or 
forms of argument, noticing the points at which they 
are specially vulnerable, and the special form which the 
objection may take. And in spite of all difficulties and 
complications, it will be found that the possibilities of 
fallacy are, fundamentally, fewer and simpler than might 
at first be supposed. Although the kind of argument 
employed may to a great extent be used as the key in 
guessing at the seat of possible error, yet the value of 
the key will be much increased by recognising the 
essential similarity of dangers which thus take on some- 
what different forms. 

II. The Types of Argument. 

§ 1. Introductory. 

In reducing the almost endless variety of possible 
arguments to a few generalised types, it must be remem- 
bered that these can only stand, towards the arguments 
actually found in use, in somewhat the same relation as 
the ' roots ' of language are (by some) supposed to stand 
towards modern forms of speech. That is to say, the 
forms of argument now commonly in use are, for the 
most part, much more complicated than these types ; and 
yet, in spite of all their complications, they are capable 
of analysis ; the roots, however modified and combined, 
can still be discovered in them. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 203 

Without some such artificial simplification of the in- 
quiry, it would be practically impossible to find a path 
at all securely through the maze of details presented : 
and with due precautions there need be no more danger 
in this expedient than in any other employment of the 
generalising or simplifying process. If, as is frequent in 
real life, a given argument employs in combination 
several of these typical forms, it is only by guarding 
against the dangers to which each part of the complex 
whole is separately liable, that we can take the whole 
in hand. Failing some method of the kind, we should 
require so large a number of special rules of evidence that 
to frame, to grasp, or to handle them effectually would 
be far beyond our power. It is probably already beyond 
the conceit of all but the most contented ignorance. 
The purpose of thus reviewing the fundamental types 
of argument is, then, that we may be able to catalogue 
their special dangers, so that, meeting with any argu- 
ment, we may obtain some guide to the points at which 
to look for weakness : and, at the same time, it is in- 
tended to bring these special dangers under a more 
general view. 

§ 2. Demonstration and Real Proof. 

For such a purpose, however, many of the distinctions 
made, both in the traditional logic and in common usa^e, 
may be left out of consideration : for example, the dis- 
tinction between 'Demonstration' and other kinds of 
Proof. 



204* FALLACIES. [Part II. 

c R,' it will be remembered, means 'Reason (or reasons) 
actually given ; ' and R may therefore either contain in 
itself both Principle and Application, or may express (or 
even suggest) only one of these, leaving the other im- 
plied. In other words, the proposition R — > T, implied 
in every argument, may mean one of two things : — 
either (1) that R includes T in its meaning, so that R 
being given, T may be known by a mere process of in- 
terpretation : or (2) that the truth of R may be accepted 
as a sign that T is able to stand against adverse criticism. 
In the former case, the argument is technically called a 
4 Demonstration,' or complete Syllogistic proof ; in the 
latter case there is, I believe, at present no strict technical 
name, but for our present purposes I propose to call such 
arguments (by far the commonest in practice) Real argu- 
ments, whether empirical (including analogical and in- 
ductive) or deductive. The distinction between Demon- 
stration and Real Proof bears a certain likeness to that 
between Tautologous and Real propositions, already dis- 
cussed (p. 42). Just as in the one case the proposition 
as a whole gives us no more information than is con- 
veyed by the S alone, so in the other case the argument 
as a whole makes no real advance upon the Reason 
given. 

The name Demonstration is perhaps not quite free 
from ambiguity. The popular notion of its meaning 
seems to be much the same as ' unanswerable,' or ' con- 
clusive,' or ' complete.' When the illogical person finds 
some theory no longer defensible, he not unfrequently 



Chap. IV.] THE EMPLOYMENT OF GUESSWORK. 205 

takes refuge in the disclaimer, "Of course I cannot 
demonstrate it, with mathematical certainty: the case 
does not admit of demonstration" — thereby implying, 
amongst other things, that if it were 'demonstrable,' 
there could no longer be any question raised about its 
truth, and that all that the disputer has done is to 
demolish this impossibly perfect kind of certainty, leaving 
the practical certainty intact. In this sense, probably, 
the following passage was written, — "However much 
one may be unable logically to demonstrate that there is 
such a thing as luck, there can be no question as to the 
fact of its existence." If the word ' demonstration ' 
means anything, it is thought, surely it must mean com- 
plete and conclusive proof. And hence, by a curious 
piece of inconsistency, the name often works round 
again, in popular usage, to mean proof which is ' suf- 
ciently ' or ' practically ' conclusive ; — as, for instance, in 
the case of a criminal caught redhanded in the act, 
whose guilt would be commonly said to be 'demon- 
strated.' 

Complete and conclusive, in a manner, Demonstration 
(in its technical meaning) certainly is. It is formally 
complete, and it is conclusive as against all who admit 
the material truth of the premisses. It is, in fact, an 
unanswerable argunientum ad hominem; and, so far as 
mankind agree about the truths which may be un- 
questionably accepted, so far but no further reaches its 
universal binding force. Hence its especial connexion, 
in the popular view, with mathematics, — the simplest 



206 FALLACIES. [Part II. 

example of its operation. The axioms of mathematics 
do not need to be reconsidered (even if we have the 
power really to do so), and so far as Demonstration 
appeals to them, so far it is conclusive as against all of 
us. But wherever any premiss, whether in a Demon- 
stration or in other kinds of Proof, meets with any doubt 
as to its material truth, the conclusiveness of the argu- 
ment depends entirely on such doubt being cleared away : 
a preliminary question is raised, which, unless answered 
satisfactorily, will destroy the material cogency of the 
Demonstration. Hence the real force of Demonstration 
rests ultimately on the same basis as that of all other 
kinds of argument, and reaches exactly the same level of 
objective cogency. Demonstration says, in fact, ' You 
admit the truth of the thesis indirectly, since you have 
already admitted the truth of this and this, which to- 
gether include or imply it.' For, unless the premisses 
are supposed to be admitted true, to assert them as un- 
assailable reasons for believing the conclusion would 
clearly constitute an insidious kind of ' begging the 
question at issue.' On this account, therefore, Demon- 
strative Proof is, as a rule, less easy to obtain than Real 
Proof ; for to obtain it, means, in fact, to obtain a person's 
consent to the conclusion without his knowledge. 

If there were any firm and sharp line to be drawn 
between absolutely binding proof, and proof tainted with 
human fallibility, each kind standing on opposite sides 
of a clear-cut chasm, then the name Demonstration might 
indeed be applied in its dictionary meaning. But as it 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 207 

is, the limits of ' axiom ' and theory ' are too ill-defined 
and undefinable, one man's meat in this respect being 
too often another man's poison. Even our senses — 
that is, our 'direct perceptions/ which always include 
an element of inference, — are, it need hardly be said, 
liable to illusion : much more so is the complicated 
mental process by which we recognise a ' fact ' as con- 
clusively certain. Many an innocent person has before 
now been " caught redhanded in the act." Accordingly, 
the nearest approach which we can make towards apply- 
ing the name Demonstration in its etymological meaning, 
and at the same time preserving its definiteness of out- 
line, is to employ it for the kind of certainty which, 
though materially fictitious, is formally complete ; which, 
though not guarded absolutely against all possibility of 
error, is guarded against it on condition of the premisses 
being materially true. And it is probably on this account 
that the name has been in Logic technically restricted to 
complete Syllogism. 

Technically then only those arguments are demonstra- 
tive in which the thesis is included in the meaning of 
the reason or reasons given. Logical necessity is merely 
the necessity of avoiding self-contradiction, for the 
purpose of preserving a consistent meaning : ■ necessary 
truth' is merely truth which is already admitted in 
another (usually a more circuitous) form. Thus the 
truth that two and two make four is already admitted 
in the full definition of the terms employed. If at least 
there be anything more in 'necessity' than is here 



208 FALLACIES. [Part IL 

claimed for it, it is something of no importance to our 
present purpose. 

Strictly speaking, Demonstration is of two kinds, — 
Immediate and Mediate (without or with a 'middle 
term'*). Hence I have said in the last paragraph 
' reason or reasons.' But in practice, when challenged to 
prove an assertion, one has seldom the chance of appeal- 
ing to a simple equivalent form which is already admitted 
true ; for the obvious reason that ' immediate inference ' is 
so extremely easy that the person admitting the equiva- 
lent form is not likely to challenge the thesis itself. 
Mere rarity of occurrence would indeed be no ground for 
neglecting all exposition of this mode of proof, if it were 
not for the fact that indirectly we have already had 
plentiful occasion to exhaust the subject so far as our 
purposes demand. The sole equivalent form of any pro- 
position, apart from such equivalence as is merely due to 
synonymous words or to variations in grammatical 
structure, is that already spoken of under the ' Law of 
Counter-indication,' and it seems unnecessary to add 
that any assertion includes a denial of all other assertions 
that conflict with it : so that the Aristotelian proposition 
I is included in A, and in E ; for this is implied in 
the full interpretation of the Maxims of Consistency. 

Now when the Reason contains expressly both a 
principle and an application of that principle to the case 
in hand, it is clear that nothing more remains to be done 
than to confront these two elements of R at once with 

* See pp. 234, 239. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK 209 

observed or admitted fact. That is to say, the operation 
of Logic as regards the original Thesis is at an end, and 
all that remains to be done is to erect, if necessary, these 
two elements (the Principle and the Application) into 
theses themselves. But occasionally it happens that such 
complete Demonstration is erroneously supposed to be 
present : and then we have either what is sometimes called 
a ' Syllogistic fallacy ', or some misinterpretation of the 
language used, or, thirdly, the vague intention of raising 
merely a ' presumption ' in favour of the Thesis. It is by 
no means always that we can tell with even approximate 
certainty which of these three causes has been in opera- 
tion, — often all three have had a share. Aristotle indeed 
declares that in his day even a mathematician * might be 
deceived by the argument, " Every figure has its three 
angles equal to two right angles : for every triangle has 
its three angles, etc., and every triangle is a figure : " and 
in Plato's Republic we frequently find such arguments 
admitted as valid : but this after all amounts to no more 
than saying that inconclusive demonstration was then in 
fact often accepted for conclusive, — a proposition true 
of modern times also: as to the exact cause of such 
acceptance, that is another matter. 

Completely demonstrative arguments, or those even 
pretending to be such, are, however, the exception, not 
the rule. They are, in fact, seldom employed in serious 
reasoning (outside certain departments of mathematics) 
but are nowadays chiefly confined to cases where some 

* Soph. El. vi. — /col oi Ttxylrai ttai o\ws oi iiria-T-ff/xoves. 



210 FALLACIES. [Part II 

more or less ingenious quibble is plainly intended, — as 
in " Dry bread is better than wisdom : for dry bread is 
better than nothing, and nothing is better than wisdom." 
The almost universal practice in these times is to save 
circumlocution by giving as Reason either the Principle 
or the Application (more commonly the latter), but not 
both together. In the case of '"chain arguments' — 
perhaps the commonest arguments of all — the Reason 
becomes as a rule still more elliptical ; for we there give 
expressly neither the Principle itself, nor its application, 
but merely the Reason which appears to be chiefly 
needed in support of one of these. Take for instance the 
not very complicated argument in favour of Home Rule 
in Ireland, that " Federalism is the finished product of 
civilisation and political ingenuity," and consider the 
further suppressed links required to complete its cogency. 
Three at least may be at once very easily distinguished, 
— the Principle that " to be the finished product of, etc., 
— > desirability," and two other propositions to complete 
the complex Application of such principle to the present 
case, — " Home Rule — > separation of Imperial from 
National and Local questions," and " separation of, etc., 
etc., — > Federalism," — none of which appear in the 
express statement. In many actual arguments, of course, 
the suppressed links are far more complicated, as in — 
" Tithes really fall on the landlord ; for the rent of tithe- 
free land is higher than that of land of the same quality 
and the same advantages of position subject to tithe," — 
where a considerable amount of special knowledge of 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 211 

the subject is required in order to properly, disentangle 
all the propositions implied. 

These chain arguments need not, however, become in 
any way a stumbling-block ; since where we do not at 
once see all the hidden implications, there is a very 
simple means ready at hand for arriving at them. How- 
ever many links there may be, they are all capable of 
being summed up in the concise expression — 
r ' If R then T, and } 
1 If not T, then not R," ) 
and we have only to call for the grounds on which this 
proposition is believed, in order to have the links set out 
as fully as we need. " How does R prove T ? " we ask. 
Thus in the example just given a person entirely ignorant 
of all the ordinary conditions of the tenure of land, 
and of all the deeper facts brought to light by Political 
Economy, would be as capable as any one else of erecting 
into a new T the connexion between the R given and the 
original T : it would take him longer, of course, to arrive 
at the rights of the matter than it would take another 
person who had already considered some of the questions 
involved, since he would have to push inquiry further 
back towards first principles ; but his present ignorance 
of the subject is only a temporary and removable bar. 

Such then being the difference between Demonstra- 
tion and the other kinds of Proof, it is clear that in 
treating the opportunities for error that occur in the 
latter we really treat those that occur in both. If, when 
either Principle or Application alone is given we can 



212 FALLACIES. [Part IL 

recognize the needs of formal adequacy sufficiently to 
avoid accepting as further assertion a supposed Applica- 
tion or Principle which does not really apply, a fortiori 
we are guarded against accepting two insufficient pre- 
misses when both are expressed. We shall accordingly 
dismiss all consideration of Demonstration as such, and 
confine attention to the forms and the dangers of what 
is here called ' Real Proof/ 

§ 3. Induction and Deduction. 

In the chapter on the Process of Proof in general,* it 
was seen that the real foundation of Proof is always the 
recognition of resemblance and difference between things 
or events known, or observed, and those which are on 
their trial, whether such recognition is based on know- 
ledge already reached, and formulated in names or pro- 
positions, or on direct observation and experiment. In 
proportion as we openly and distinctly refer to known 
principles — already generalised knowledge — is Proof de- 
ductive: in proportion as we rapidly and somewhat 
dimly frame new principles for ourselves from the cases 
observed, is Proof inductive, empirical, or (in its loosest 
form) analogical. 

The whole history of the rise and growth of know- 
ledge, it has been also already remarked, is a record of 
fruitful rivalry and interaction between two opposite 
processes. Observation of facts has demanded theory — 

* Part i. chap. v. 



Chap. VL] THE EMPLOYMENT OF GUESSWOKK. 213 

statement of ' laws ' or uniformities — to explain, and 
even to name, the things and events observed : theory 
in its turn has always been more or less liable to the 
purging criticism of 'fact.' In the strictest sense, of 
course, Deduction and Induction are modes of Inference, 
not of Proof at all. Strictly speaking, all Proof, so far as 
really Proof, is deductive. That is to say, unless and until 
a supposed truth can be brought under the shadow of some 
more certain truth it is merely self-supporting, or circular. 
Unless we have some more comprehensive and better 
tested generalisation within the sweep of which to bring 
our thesis, we reach no foundation broader than itself ; 
no assurance beyond what may be derived from the fact 
that nothing has yet been found to contradict the theory. 
But yet there is a meaning in the distinction, and, with 
certain limitations and apologies, I propose to make some 
use of it. Although the dependence of any Thesis on its 
Reason must be rationalised — i.e. must have the under- 
lying principle made clear — before the testing operation 
can be called complete, yet in regard to special dangers 
it makes considerable difference whether the principle is 
at first definitely apprehended or not, — whether (as it is 
commonly expressed) the Proof professes to rely upon 
Laws known or supposed to be true, or upon facts ob- 
served or supposed to be observed. We must distinguish 
then, as far as possible, between that kind of Proof which 
rests openly and distinctly upon already generalised 
knowledge — Deductive Proof, — and that which rests 
upon what may be loosely described as ' isolated facts,' 



214j FALLACIES. [Paet II. 

or 'perception of resemblance and difference/ or 'ob- 
servation and experiment/ or ' circumstantial evidence/ 
or however the phrase may run, — that which is com- 
monly known in its highest form as Inductive Proof, and 
in its lowest form as the Argument from Analogy. 

The required limitations in preserving the distinction 
appear to be, in the first place, a clear recognition that 
although in Induction the Principle, or Law, connecting 
the cases observed with those inferred is in the case of 
Inference commonly dropped out of sight, or at least left 
highly indistinct, yet the whole cogency of Inductive 
Proof depends upon the extent to which such Principle 
is first rendered definite and then confronted with ob- 
servable or admitted fact. So long as the Principle is 
left indistinct, we may be fighting under false colours — 
misled, that is, by false analogies, or hampered by dis- 
tinctions without a difference — in extending our know- 
ledge to the supposed ' parallel cases/ or in drawing our 
line exactly where we do. There is, in fact, probably 
no more fertile source of real (as opposed to merely 
verbal) fallacy than just this neglect, or dread, of ' ra- 
tionalising ' our beliefs, — of bringing their underlying 
principles out into the daylight. The name Inductive, 
then (as also ' empirical ' and ' analogical '), is properly a 
name of a mode of Inference. It describes the fact that 
in arriving at our Thesis the Principle was left more indefi- 
nite than if we had reached the Thesis deductively. The 
provinces of Analogy, Induction, and Deduction are thus 
merely rough divisions on a scale : the more definite the 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 215 

Principle the more the inference possesses the deductive 
character, the less definite the nearer it approaches to 
loose Analogy. But equally in deductive and in analo- 
gical arguments, in order to rationalise the belief the 
underlying Principle must be made definite. The chief 
value of the distinction, for purposes of Proof, is that it 
serves to call attention directly to that part of an argu- 
ment which stands in pressing need of careful examina- 
tion : meeting with an empirical argument we may often 
shorten the process of testing it by inquiring in the first 
place what the underlying Principle really is, — how far 
it will bear reduction to definiteness and comparison 
with fact. Empirical arguments are, too, so far as em- 
pirical, free from mere snares of language, — which play 
so large a part in all deductive proof : their chief danger 
may be summed up as the adoption of some theory with- 
out examining, or perhaps even seeing, the alternatives. 
But this will be more fully discussed presently. 

The second difficulty in preserving the distinction lies 
in the fact that as a rule the Empirical and Deductive 
processes are found in combination, both being employed 
on the same subject-matter. Not only does Inductive 
Proof — in its higher forms — make large use of Deduc- 
tion, for verifying the hypotheses put forward, but all 
Proof, however professedly deductive, is in the habit 
(at least where the generalised knowledge is not very 
firmly established in the individual mind) of drawing 
much confidence from successful prediction, and even 
from merely congruent facts. Some Free-traders, for 



216 FALLACIES. [Part II. 

instance, lacking robust faith in the abstract propositions 
from which that theory may be deduced, or failing to hold 
them clearly in memory, are apt to feel an accession of 
security when statistics ' prove them right ; ' and weak 
or vague generalisations, such as that ' Roman Catholi- 
cism and national poverty go hand in hand/ commonly 
draw what strength they possess jointly from the two 
sources, prejudice (i.e. 'known law') and observation. It 
would certainly be hard to find a single instance of in- 
ference, within historic times, in which we could say 
beyond all doubt that Deduction was wholly wanting or 
had contributed nothing to the belief; and since any of 
the causes of a belief are liable to be relied upon as reasons 
on reflection, it is rare to find professed empirical proof 
entirely free from the deductive element.* Sometimes, 
no doubt, from one cause or another, either method may 
dwindle into insignificance beside the other. A great 
many people, for instance, are inclined to settle the 
claims of ghost stories deductively ; — partly perhaps 
because they find as a rule that their hands are more or 
less hampered and their eyes rendered more or less use- 
less, before they are allowed to begin experimentation. 
On the other hand, in Meteorology, from a deficiency of 
known laws we are thrown very much upon bare facts 

* Even in attempted Proof we commonly find the two processes 
mingled, as where Parson Lingon argues in favour of cock-fighting, not 
only that under it " England had been prosperous and glorious," but 
that " the practice sharpened the faculties of men, gratified the instincts 
of the fowl, and carried out the designs of heaven in its admirable device 
of spurs." 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 217 

as recorded in statistics ; what certainty we have regard- 
ing the weather is mainly empirical. In all cases of real 
proof, however, it is probable that nowadays both pro- 
cesses play some part. 

These two considerations make it, of course, extremely 
difficult in practice to label every argument at once with 
one or the other name. Sometimes, as where the Reason 
is a direct statement of the Principle itself, or again where 
it consists of a record of some experiment, no hesitation 
need practically be felt as to where the danger lies ; but 
in a large number of cases we have no means of deciding 
whether the argument may best be classed as empirical, 
or deductive, or both. 

In those logical treatises in which Inference and Proof 
are not clearly distinguished, and where consequently the 
distinction between Induction and Deduction occupies 
a very prominent place, there seems to be a desire to 
restrict the name of Inductive Proof as far as possible 
to the establishment of latus by means of isolated facts, 
Analogical Proof to the establishment of facts by means 
of resembling facts, and Deductive Proof to all other 
cases. But we have seen that both Principle and Appli- 
cation are required for all completed proof whatever: 
that is, until both are brought to daylight and examined, 
the testing of the Thesis remains unfinished. Sometimes 
— i.e. in Demonstration — both Principle and Application 
are expressly given by the Reason ; at other times one or 
the other only. But yet it will not do to say that wher- 
ever the Principle is merely implied we have a clear case 



218 FALLACIES. [Part II. 

of Empirical Proof, since it is sometimes through extreme 
familiarity, rather than through insufficient definiteness, 
that its statement is suppressed; as where we argue 
" The Pope is fallible, since he is human." In many such 
cases the Principle relied upon might well be definitely 
enough apprehended to warrant our calling them cases of 
deductive proof. 

What then, it may be asked, is left of the distinction 
at all ? Have not these innocent limitations and 
apologies in fact proved too much ? If we cannot tell 
for certain in the given case whether the argument is 
properly an empirical one or properly deductive, why 
keep the names and make a pretence of using them ? 

In the first place, we are here intentionally seeking to 
make the best use of the guesswork system of detecting 
Fallacy, and with that view may be thankful for even 
rough distinctions suitable to the purpose. Nor, because 
the distinction breaks down when pressure is put upon 
it, need we consider it wholly worthless. It possesses a 
solid core of applicability, and if we can be content to 
use it as a rough guide in finding the weak point of an 
argument, much value may still be extracted from it in 
economy of time. 

Again, if the names Induction and Deduction make us 
think of Inference rather than of Proof, we are not 
obliged to use them. However we choose to name the 
two different kinds of arguments, the distinction between 
them has a certain real importance, as already shown; 
and all that is intended to be done with it is to recognise 



Chap. VI J THE EMPLOYMENT OF GUESSWORK. 219 

that so far as the given argument may be seen to belong 
to one or the other class, so far we are already some way 
on the track of ' special dangers/ 

A thesis, then, whether abstract or concrete, is some- 
times supported by bringing forward a congruent fact, 
or a number of congruent facts : in this case the thesis, 
when abstract (as e.g. the law of Gravitation, or of 
Natural Selection) is usually called a theory. An abstract 
theory is offered both as an explanation of the facts on 
which it rests and as a means of prediction in the future, 
thus basing a general law upon individual facts observed. 
When the thesis is concrete it is rarely called a theory, 
but professes to argue direct from case to case, by what 
is called Analogy, or Resemblance, or Extension to parallel 
cases. 

Or, secondly, a Thesis, also either abstract or concrete, 
is sometimes supported by appealing, expressly or other- 
wise, to an already recognised law. Here the Thesis 
(except when explanatory) is not as a rule called a theory, 
— probably because that name carries with it by custom a 
shade of uncertainty, which seems to throw unnecessary 
doubts upon the ' already-recognised law:' it is occasionally 
called a 'deduction/ but more often has no distinctive 
title. As to the nature of the Reason, sometimes the law 
itself is expressly mentioned, but more commonly the S 
of the thesis is labelled with some name, or said to have 
acted or suffered in some particular way which is ' known ' 
to carry certain consequences. In other words, whenever 
the Thesis professes to be deduced from some already- 



220 FALLACIES. [Part II. 

framed law, the Reason either expressly mentions this 
law, leaving its application implied, or it appeals to some 
sign, expressly asserted to be present in the given ease, 
leaving the universal trustworthiness of such sign implied. 
Accordingly, the two main kinds of argument may be 
called respectively the Argument by Example and the 
Argument by Sign. In the former we rely primarily on 
' facts ' observed, no law to cover the case being as yet 
distinctly admitted; in the latter we make use of the 
recognised results of past observation, whether registered 
in express propositions or merely taken for granted in the 
meaning of the names employed. 

§ 4. Certain Minor Distinctions* 

Before further subdividing these two main forms of 
argument, it will be well to notice briefly certain other 
distinctions which are sometimes made, but which mark 
differences that are quite unimportant for our purpose. 
Thus we have seen that the distinction between conclu- 
sive and presumptive proof, though useful perhaps before 
inquiry begins, is altogether too loose for adoption into 
Logic. In one sense no proof is conclusive, in another 
sense unless proof professes to conclude the inquiry it is 
not proof at all. Really, the distinction seems to be 

* This section contains several technicalities which could not be 
explained, or omitted, without considerably lengthening the exposition, 
and it seemed desirable to save space as much as possible, since the 
section is not essential to the main thread of our subject. The techni- 
calities can be easily found in any logical text-book. 



Chap. VI] THE EMPLOYMENT OF GUESSWOEK. 221 

intended to mark roughly the difference between a Thesis 
asserted and one that is merely suggested; and such 
hesitating theses lie quite outside our present interests. 
Further, certain names, such as circumstantial evidence, 
are almost synonymous with others that will here be 
employed; empirical evidence including circumstantial 
evidence as the whole includes the part. Again, 'testi- 
mony/ ' hearsay evidence,' etc., though marking distinc- 
tions valuable perhaps for some purposes, are varieties 
which do not readily admit of any special treatment, 
except where there exists, as in Law, some authority 
competent to lay down strict rules with a merely average 
balance of good result. Logic is less pressed for time 
than Law, and can afford to decline to generalise where 
generalisation is only so roughly justified. 

Again, there is the distinction between hypothetical 
arguments and those which are commonly called cate- 
gorical. A hypothetical argument, of whatever kind, is 
simply one in which the major premiss (the Principle) 
takes the form of a hypothetical proposition The dif- 
ference between a categorical and a hypothetical propo- 
sition is, we have seen, merely a grammatical one, 
conveying at least no difference of meaning that is of 
importance to our view of Logic. Any categorical argu- 
ment may therefore be expressed in hypothetical form, 
and vice versa. While, however, the danger in hypo- 
thetical and in categorical arguments is essentially and 
fundamentally the same, the language in which it has to 

be described is, under the predication view, somewhat 
11 



222 FALLACIES. [Part II. 

different. The hypothetical proposition divides into Ante- 
cedent and Consequent more naturally and readily than 
into S and P, and accordingly the ' middle term ' of a 
hypothetical argument is hard to find, — or rather it 
seems almost a straining of language to call it a middle 
term at all.* In a categorical argument the middle term 
of the Syllogism involved is often difficult enough to 
disentangle clearly, f but since in hypothetical arguments 
the middle ' term ' is itself a proposition, namely, the 
Antecedent (or, for a negative conclusion, the denial of 
the Consequent) of the Principle, any search for the 
middle term, as such, is more often a source of confusion 
than of help. In fact, in all cases of difficulty, translation 
from the categorical into the hypothetical form will, I 
think, be found the easier plan, for then we have merely 
to see whether or no the minor premiss properly affirms 
the Antecedent (or denies the Consequent), or improperly 
denies the Antecedent (or affirms the Consequent). The 
fallacy of 'affirming the Consequent* in hypothetical 
argument is essentially the same as that of employing 
an ' undistributed middle ' in a categorical one ; and in 
like manner it may be shown that ' denying the Ante- 

* See also Bain's Logic, bk. i. chap. iii. sect, 30. 

t As, e.g. in the argument from difference — Cesare or Camestres*— 
where, in order to bring M to the position required, we have to contra- 
posit the major premiss. Let the T be ' Whales are not fishes,' and the 
R ' they cannot remain always under water,' the principle involved is 
clearly, ' Fishes proper can remain, etc. ; ' but it is only in the contra- 
positive form — viz. ' That which cannot remain, etc., is not a fish,' that 
we can bring the middle term into the position required. 



Chap. VI] THE EMPLOYMENT OF GUESSWORK. 223 

cedent* is essentially the same as 'illicit process of the 
major.' But in order to describe the danger in these 
cases in the words that are most simply and naturally 
applicable to them, it seems better to preserve the dis- 
tinction, merely noting that it is of grammatical rather 
than logical interest. 

Of further varieties of argument the complete list 
would be a very long one. Numerous small distinctions, 
unnecessary for our purposes, have been made from time 
to time. Thus we have the nineteen valid moods of the 
Syllogism (several of which never really occur in prac- 
tice), or again the argumenta ad personam, ad verecun- 
diam, ad populum, etc. — names which imply a large 
amount of insight into other people's motives. As regards 
the Syllogistic moods, while preserving to some extent 
the differences on which they are founded, we may reduce 
their number considerably. In fact, under the liberal 
treatment here adopted towards the exact words in 
which any assertion may happen to be clothed, some 
simplification in this respect follows of necessity. Thus, 
while we shall be obliged * to take some account of the 
difference between an affirmative and a negative Thesis, 
we do not need to distinguish in every case a negative 
proposition, as understood in the Aristotelian scheme 
from a positive one ; and again, every ' particular ' pro- 
position, so far as it makes a tangible assertion at all, is 
negative in our sense. A negative proposition, as we 
have elected to understand it, is only a proposition which 

* See p. 243. 



224 FALLACIES. [Part II. 

intends to deny some positive assertion already made 
or believed, not every proposition which happens to 
contain the negative particle, in however close connexion 
with its verb. The traditional mood Celarent, for ex- 
ample, is probably hardly ever used for Disproof, Camenes 
probably never used at all. And, as will be seen later,* 
all the fourteen syllogistic moods with the conclusion in 
I or O may be conveniently reduced to two. 

The remaining distinctions we shall have to make 
will be entirely within the two main types, the Argument 
by Example, and the Argument by Sign ; and they are 
set out in a table (IV.) in the Appendix (E), which may 
be usefully kept in view during our discussion of the 
special types of argument. 



§ 5. The Argument by Example. 

What is here called the Argument by Example, or by 
' Congruent Fact/ is not quite the same as that which 
is commonly known as Proof by Circumstantial Evidence, 
though closely similar : on the surface at least, the latter 
mode of argument relies upon facts (i.e. circumstances) 
which together confirm the Thesis. It is difficult, indeed, 
to say precisely what is '. commonly known ' under the 
name Circumstantial Evidence, since popular usage seems 
to vary. The common acceptation of the term is, how- 
ever, almost certainly, somewhat narrower than that to 

* Cf. infra, p. 241, and Appendix (C). 



Chap. VI.] THE EMPLOYMENT OF GUESSWOKK. 225 

which its literal (i.e. derivational) meaning would point. 
Literally, circumstantial evidence should include, one 
supposes, every case of proof from the circumstances (or 
aggregate of isolated facts) observable or known : so that 
(1) a geological explanation, founded on Nature's foot- 
prints, or (2) our opinion of a neighbour's character, 
founded on his general conduct, or (3) a political pre- 
diction, founded on the signs of the times, or (4) any law 
of nature, founded on wide observation and experiment, 
would all equally come under the title. But no doubt 
such an employment of the term would be considered a 
straining of language. The name circumstantial evidence 
shows a decided tendency to restrict itself, in common 
usage, if not solely to the case where a crime is traced 
home to the criminal by means of the marks that he (oi 
his act) has left behind him, at any rate to proof of the 
cause of a concrete fact where the evidence of eye- 
witnesses cannot be obtained, and where the circum- 
stances are singly weak. In Law, of course, the reason 
for the importance given to this distinction is mainly 
the recognition that ' facts may bear more than one 
interpretation,' while direct testimony is, in the large 
majority of cases, free from all danger except that of 
deliberate perjury. 

Under Proof by Example, however, will be here in- 
cluded all cases where a proposition, whether abstract or 
concrete, is supported by the production of a fact, or of 
facts, which are simply given as agreeing with the theory, 
or as forming cases under it, when at the same time it is 



226 FALLACIES. [Part II. 

recognised that there is as yet no definitely known Law 
in the matter, to which appeal can be directly made. 
The primary danger in all such cases is the same, — 
namely, that the fact or facts produced will admit of 
some other interpretation than that put upon them by 
the theory. But this danger takes certain special 
shapes, which it will be worth while to consider more in 
detail. The subdivision to be made under the Argument 
by Example is that into : — 

(a) The Argument by Analogy. 

(6) Proof of a Generalisation, by the facts which it 
is intended to explain. 

The first of these is what we have already had occasion 
to notice (p. 104) as ' extension to parallel cases ; ' the 
second embraces what are commonly known as the pro- 
blems of Induction, — so far as Proof is concerned. 

(a) The Argument by Analogy. 

Analogical reasoning, or the argument from indistinct 
resemblance, is one of the most difficult subjects to treat 
with satisfactory completeness, since arguments of ap- 
parently the most diverse forms are apt to contain more 
or less of it, and on the other hand we rarely meet with 
a case of open reliance on Analogy pure and simple. 
That is to say, where we do find Analogy unmistakably 
employed, there is also commonly a strong inclination 
either to soften the force of the assertion made in the 
Thesis, so that the process should be viewed less as an 



Chap. VI-1 THE EMPLOYMENT OF GUESSWORK. 227 

attempt at proof than as a mild suggestion ; or else to 
put forward the analogy rather by way of illustration 
than as evidence. 

It was not without a reason that we avoided choosing 
a symbol for the assertion of indistinct resemblance 
between S and £&. For essential resemblance, it will be 
remembered, we found * a symbol (the now familiar 
— >) ;. but for the too common assertion ' S is strikingly 
like §3/ our scheme provides no place. The reason is 
that this vague assertion can only be conceived as ac- 
quiring a practical value for Proof (valuable though it 
may always be for Discovery) by emerging from its safe 
obscurity through the claimed resemblance ceasing to be 
any longer indistinct. 

Resemblance, it is on all hands admitted, varies in 
degree. A given individual, we say, for instance, is 
more like his father than his mother ; distantly re- 
sembles a cousin; and still more faintly, a stranger, a 
savage, or some particular animal. A cloud in the 
sky may bear a fancied resemblance to some familiar 
object, but not so close a resemblance as one pea bears 
to another. Now the only manner in which gradual 
variation can be represented seems to be by means of 
numbers, — or at least of pictures with measurable pro- 
portions, — and measure implies the conception of relative 
number. Hence, it seems, we are driven to say that 
resemblance varies in some manner expressible (if at all) 
by means of numbers. 

* See p. 64. 



22S FALLACIES. [Part H. 

To meet the needs of accurate comparison, we have 
accordingly established the familiar phrase 'points of 
resemblance.' John resembles his father in the eyes, 
or hands, or hair : he has his mother's accent, and a touch 
of his grandfather's gout : holds the same opinion as his 
friend on a certain important question ; has a less hasty 
temper than his enemy ; and it is in ' expression ' only 
that he resembles a mastiff or a bull. 

But what are these so-called ' points ' ? Are they 
simple units, which have only to be counted, for and 
against, in order to work the sum by straightforward 
addition and subtraction ? I fear it is not always easy to 
avoid all taint of this plausible error. Accurate measure- 
ment seems at first sight to demand equality of units. 

The fact appears to be, however, that no so-called 
' point ' of resemblance or difference is known to exist 
which is not in theory further analysable, and few that 
are ultimate even to the naked eye. The colour of the 
eyes, for example (to choose out of the list just given 
the point which seems on the whole least likely to yield 
further component parts), may be broadly classed as 
blue or brown or black and so on; but it can hardly 
be disputed that between these rough distinctions, end- 
less shades of difference are possible. As for accent, 
liability to gout, similarity of opinion, or of temper, or 
of expression, each of these is plainly seen to be built up 
of innumerable components; the numerical difficulty is 
only verbally solved and really shelved, by determining 
to treat any given ' point ' as ultimate. 



Chap. VL] THE EMPLOYMENT OF GUESSWOEK. 229 

If we cannot then arrive at valuable results by simply- 
counting the points of resemblance and difference, as we 
count black and white balls in a ballot-box, what other 
resource is open ? Only one ; namely to estimate as well 
as we can their relative importance as regards the matter 
in hand. For this purpose the phrase ' essential points ' 
has been invented. ' Essential resemblance ' means ' re- 
semblance in the point (or group of points) M,* which 
is essential ; ' and by essential is here simply meant 
1 sufficient to prove a certain other assertion ' to which 
reference is thus indirectly made. Without this indirect 
reference to some further proposition, the phrase ' essen- 
tial resemblance' becomes, not perhaps quite meaning- 
less, but deprived of any meaning that exists in definite 
shape: for to reduce it to definiteness would be just to 
state wherein the essentiality consists. It has been 
sometimes said, for instance, that the State essentially 
resembles a family ; and vaguely every schoolboy can 
see the likeness at once. But beyond a mere oriental 
delight in simile for its own sake ; and beyond the hazy 
satisfaction which is still apt to follow even the cheapest 
attempt to classify ; when we push the question home, 
and ask what exactly is intended to be conveyed by the 
assertion, we find ourselves really hoping, by means of 
the asserted resemblance, to register our right of arguing 
(within certain indefinite limits) from family to State ; 

* The symbol M (Middle term) is here chosen in reference to the 
manner in which the fundamental structure of the analogical argument 
corresponds to that of the deductive one. See also pp. 232, 234. 



230 FALLACIES. [Pabt II. 

that is, of saying that since some given assertion may 
be made about the former it may also be made about the 
latter. It is this further assertion, whether clearly 
apprehended as the purpose or (more commonly) not, 
to which the ' essential ' refers : and an ' essential point ' 
is a resemblance or difference, wide or narrow, complex 
or apparently simple, that may be used as a sign of the 
truth of such proposition. 

As yet, however, the difficulties in fully understand- 
ing the analogical argument are hardly more than begun. 
And first, as to the symbolic expression ; here some care 
is needed in order to avoid ambiguities. It clearly will 
not do to use S and J£> as the terms of both propositions, 
the Thesis and the Reason; but with the aid of the 
symbol Z in addition, we can sufficiently express all that 
is necessary. If we also use the symbol for Re- 
lation in general, the universal form for the analogical 
argument would run as follows : — 

(Thesis) S Z ; for 

(Reason) §b Z.* 

This, it must be confessed, just as Mill's formula on 
which it is based,-)- is a statement simplified artificially 
to the utmost. An actual analogical argument may be 

* It should be noticed, however, that this formula is only valid on 

the condition that the symbol means approximately the same in 

Thesis and Reason. 

f Mill's formula is stated, however, as if discovery, not proof, were 
chiefly contemplated. It runs, " Two things resemble each other in 
one or more respects ; a certain proposition is true of the one, therefore 
it is true of the other." 



Chap. VI.] THE EMPLOYMENT OF GUESSWOKK. 231 

complicated by failure of complete identity between Z 
m Thesis and in Keason, or even perhaps between the 
respective copulas.* Or again, Analogy is very commonly 
employed as part of a full deductive process, as in 
" Colonies ought not to rebel against the mother-country, 
since they are (so to speak) its children, and (it is an 
accepted law that) children ought not to rebel against 
their parents." Every kind of argument, in fact, may 
have an analogical element in it, and wherever the 
analogical element is present the danger is to that extent 
the same. But this special danger will be spoken of 
later ; at present we have only to set out and describe 
the various kinds of argument. 

A more serious difficulty may be stated as follows : 
If, as appears, what is really relied upon in the argument 
by Analogy is a supposed ' essential resemblance ' between 
S and Jfc, and if by essential resemblance is meant 
resemblance in the point M, such point being claimed as 
a sign for the purpose required ; wherein does the attempt 
to prove by analogy differ from the purely deductive 
argument ? Clearly, it may be said, unless the resem- 
blance is declared essential for the purpose in hand (i.e. 
for proving the Thesis), there is nothing to show the 
relevancy of the argument ; until the points of resem- 
blance are recognised as such, how can we even begin to 
inquire whether they are important or wholly trivial; 
and if their possible triviality is still an open question, 
whence our confidence in their binding force ? 

* The ' copula ' is the sign of relation. See p. 54. 



232 FALLACIES. [Part II. 

The answer must be that this is exactly the question 
which Logic has to put to the person whom an analogy 
convinces. The difference between the analogical and 
the deductive arguments is a difference in the degree of 
distinctness with which the existence of the link M, and 
the fact of its being a truly important link, are recognised 
and appealed to. We need a name by which to describe 
the cases where these two opportunities for .error have 
been left to take care of themselves, — where ready and 
generous faith, rather than the cold and grudging spirit 
of strict inquiry, has been in operation, — and for this 
purpose the name Analogical Reasoning has won a firm 
place in our terminology. By analogical reasoning we 
denote what may be called embryonic deductive argu- 
ments, — arguments which are as yet in happy uncon- 
sciousness of the troubles in store for them later. 

The solution of the seeming paradox is therefore not 
difficult to find. The argument from analogy is, properly 
speaking, not so much a mode of attempting proof, as 
a mode of attempting to dispense with the serious labour 
of proving. It lies at that end of the scale of cogency 
which is furthest from Demonstration. Instead of win- 
ning its results openly, in the face of hostile criticism, 
it prefers the easier course of simply claiming already to 
hold them safe. It is only this claim which causes the 
puzzle just noticed; we are apt to forget that a claim 
may be made without any valid foundation. 

In this connexion, there remains one further difficulty, 
though not of any great importance. It will perhaps be 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 233 

doubted at first sight whether the analogical argument 
should properly be considered to come under Proof by 
Example as here understood ; since, the Thesis being itself 
the ' theory/ the Reason is not a ' fact agreeing with the 
theory/ except on condition that the analogy holds good ; 
which condition cannot be simply taken for granted with- 
out begging the question. ' £& — > Z ' (e.g.) is only a fact 
agreeing with the theory that S — > Z, on condition that 
there is essential resemblance between S and §b ; and 
the question whether or no this essential resemblance 
exists is just the turning-point of the argument. But 
the reason for treating Analogy as Congruent Fact is 
that inasmuch as the employment of an analogical argu- 
ment implies in itself that the analogy is supposed (by 
its employer) to be a valid one, wherever analogy is 
appealed to as proof it is clear that R is given as being 
a fact agreeing with the theory ; inasmuch as the case 
given is supposed by the arguer to be a case in point, 
the argument is brought forward as resting on a fact 
agreeing with the theory. 

The central type of Analogical reasoning is, then, 
that which we have already briefly noticed above as 
' Extension to parallel cases/ Case S and case Jfe being 
seen to be 'similar/ a certain assertion true of the one 
is supposed to be true of the other. If the sugar trade 
is to be protected, why not the iron trade or the cotton 
trade ? Since the Irish Church has been disestablished, 
why not the English Church also ? Such examples 
as these, however, lie on the borderland between the 



234 FALLACIES. [Part II. 

arguments from analogy and from sign. The technical 
distinction between the argument from analogy and 
the deductive argument from sign or mark (or middle 
term) being that in the former the exact points of re- 
semblance and difference between the things compared 
are admittedly not yet distinct, it follows that so soon as 
the details of resemblance become clearly recognised as a 
warrant for considering the cases parallel, these points of 
community become at once a sign relied upon, and the 
argument rises to the deductive rank. Thus in the 
instances just given, if the sole (or sufficient) point of 
resemblance claimed be the fact that both are trades or 
that both are national Churches, then the assertions that 
the sugar trade ought not to be protected or that the 
English Church ought to be disestablished, are based no 
longer on mere analogy but on implied principles under 
which they are brought by means of the respective signs 
or middle terms. The case of the sugar trade is in this 
way referred to the recognised principle that protected 
trade is on the whole uneconomical ; the case of the 
English Church is referred to a precedent supposed to 
have been created (i.e. a principle supposed to have 
already received tacit recognition) by what has gone 
before. 

(6) Proof of Law from Fact 

The second mode of Proof by example is where the 
example or examples given are not supposed parallel 
cases to the theory, but instances, and if possible ' cru- 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 235 

cial ' * instances, of the operation of the supposed law. 
And, first, there is a further simplification to be made, 
after the pattern of that used by Mill in framing a uni- 
versal formula for Analogy. The generalisation which 
appeals to facts as evidence may, as we have seen above, 
either be expressed directly as an abstract proposition, 
or lie hid under cover of a concrete or abstract-concrete 
one. The attempt to prove, for example, that S (a known 
concrete event) was causally connected with §3 (whether 
the latter be also known to have existed or not) by 
means of some fact merely agreeing with such theory, — 
such as that S immediately preceded or followed §3, 
either in this case or on past occasions — belongs properly 
to this mode of argument just as truly as the attempt to 
prove by the same means the simple direct generalisation 
that S is (in general) thus causally connected with §5. 
In other words, the evidence produced for any assertion 
may conceivably be (is sometimes) of an empirical kind. 
In supporting any variety of thesis, the exact law, or 
outcome of conflicting forces, relied upon, may be so 
dimly conceived that to call the process in its present 
stage deductive w r ould be to confuse a very important 
distinction, while any attempt to search first for the 
faults to which deductive proof, as such, is mainly liable, 
would be a waste of time. 

This being the basis of the distinction, we shall find 

* A crucial instance, in its modern sense, may be defined as any 
single instance deemed sufficient to prove a law : as in many cases of 
Proof under the method of Difference. See Appendix (B) , p. 346. 



236 FALLACIES. [Part II. 

that, in attempting to frame a typical formula for the 
inductive argument, it is best to take for the Thesis an 
abstract proposition. Not only are such arguments the 
kind in which the evidence is as a fact most frequently 
empirical, but that in which it is most rightfully so : since 
a concrete proposition that rests on merely empirical 
grounds has, and is widely recognised as having, a merely 
provisional support ; while it is equally clear and also 
sufficiently widely recognised that our deepest basis for 
abstract law is concrete fact. To deal with concrete 
subject-matter successfully, in the complexity in which 
it actually occurs, — which complexity is ever becoming 
more manifest as our view opens out and hidden dif- 
ferences come to light, — we need at least some glimpse 
of the uniformities concerned, some knowledge of what 
may be expected a 'priori ; and this whether the concrete 
Thesis is explanatory, classifying, or predictive. In 
practice it is safe to say that wherever a concrete Thesis 
is supported by appeal to congruent facts alone, the first 
step towards testing the value of the evidence must be 
to get the supposed underlying laws clearly stated ; and 
that where an abstract-concrete proposition is thus sup- 
ported, it is the abstract element in it which stands first 
in need of proof. 

After what has been already said on the subject of 
Analogy, this more direct kind of generalisation needs 
little further preliminary notice. Whereas in analogical 
reasoning the leap from one supposed parallel case to the 
other is made with only a dim recognition of the law 



Chap. VI.] THE EMPLOYMENT OF GUESSWOEK. 237 

(M — > Z) which should bind the cases together, here we 
have the law itself directly set up as Thesis. §b has been 
observed in a certain connexion with Z, in certain cir- 
cumstances which seem to warrant our saying not only 
that when (if ever) we meet with g> again we may look 
for Z, but that M was that particular element of %*> which 
was essential, and that the wider law M — > Z can hold 
its own against all but unpractical doubts. 

Any ' thing ' we like to name, — let us here name it §b 
— is analysable into component circumstances. Let §^, 
for example, be that event called the arrival of a ship at 
St. Kilda. Some time ago "it was a general belief at 
St. Kilda that the arrival of a ship gave all the inhabi- 
tants colds." * Let ' unusually numerous colds among 
the inhabitants ' be represented by Z. The inhabitants, 
then, we are told, commonly believed the truth either of 
the simple law Jfe — > Z, or possibly (if the material 
framework of the ship itself be denoted by M) the law 
M — > Z. But this easy explanation did not satisfy 
Dr. John Campbell, and he began to analyse £3 a little 
more deeply, and to ask what distinguishable circum- 
stances there were, forming part of that which was 
broadly described as ' the arrival of a ship ; ' and after 
taking " a great deal of pains " he ended by explaining it 
" as the effect of effluvia arising from human bodies." "VVe 
are not told more definitely what he meant by this, or 
why the arrival of a single ship at the harbour should 

* Dr. Paris, Pharmacologia, p. 89, quoted by Prof. Fowler, Inductive 
Logic, p. 310. 



238 FALLACIES. [Part II. 

mean so great a difference in the amount of effluvium in 
the island, but at any rate such was his explanation ; 
and if we denote ' effluvia arising from human bodies ' 
by N, the law at which he arrived was either ' N — > Z,' 
or 'gb, when N, — > Z.' 

Dr. Paris, however, either himself discovered, or at 
least quotes and endorses the discovery of, another 
element inseparable from £§, and in his view more im- 
portant as regards Z. This was the fact that " the situa- 
tion of St. Kilda renders a north-east wind indispensably 
necessary before a stranger can land." Let N.E. wind 
be represented by 0. "The wind," he adds, "not the 
stranger, occasioned the epidemic ; " or, in other words, 
he views the real law as O — > Z. This law, it may be 
usefully noticed in passing, was not then discovered for 
the first time. O was already known as a vera causa of 
Z, while M and N were not. If we had no known laws 
already, discovery of explanations would be a slower 
process than at present. But Dr. John Campbell had 
left the supposed law in an unsatisfactory condition : the 
assertion §■> N — > Z was in possession, and it had to be 
made to face a hitherto unsuspected alternative, — that 
which Dr. Paris suggested. 

It seems hardly necessary to remark that the symbols 
M and Z were only chosen in order to show more clearly 
the connexion between Induction and Analogy. But in 
framing a formula for the inductive argument, we may 
now return to S and £&, without any danger of misinter- 
pretation. I do not see how to put the whole inductive 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 239 

argument into symbols ; but we may state it in a con- 
veniently short form as : — 

S (universally) — > §j : for here are (one or more) 

cases of which this law is the best explanation : 

proper precautions having been taken against all 

rival theories. 

The discussion of these proper precautions will be more 

in place when we speak more directly of the dangers of 

Empirical proof At present there remain the deductive 

arguments to set out. 



§ 6. The Argument by Sign. 

In speaking of Analogy, we have already sufficiently 
noticed the indistinctness of the line between this and 
Deductive Proof, and the manner in which the analogical 
argument becomes deductive as soon as the points of 
supposed resemblance between S and gb are definitely 
apprehended as a warrant for the inference And just 
as the analogical argument may apply to any kind of 
subject-matter, so may the strictly deductive argument. 
We may attempt to prove or to disprove either an abstract 
or a concrete proposition, and either an explanatory, a 
classifying, or a predictive one, by means of a definite 
middle term. And, further, the nature of this middle 
term, or link, must also already be sufficiently obvious. 
If it is to be really a link, it must be a sign ; or, in other 
words, it must be known to us (or expressible) as the S 
of an assertive proposition. 



240 FALLACIES. [Part II. 

It remains to be added, however, that although in 
every deductive argument M may certainly be viewed as 
a sign, thi3 is not always the most direct description of 
it that can be given. Various types of deductive argu- 
ment are distinguishable, and it is only where the Thesis 
is affirmative that we really gain much by resting our 
case on plain, straightforward indication. Thus, where 
the Thesis is ' S (or This S) > Jfe,' if we know already 
the law that M — > gfe, M is well described as a mark 
or sign which it should be our aim to show that S pos- 
sesses. And, on the other hand, if * S — > M ' be given 
as a reason, the relevancy of such reason plainly depends 
on the trustworthiness of M as indicating £§. This for- 
mula, it will be seen at once (namely ' S — > Jfc> : for 
S — > M, and M — > §j '), corresponds to the ancient 
syllogistic mood Barbara (or to Celarent, where the E 
conclusion is affirmative in the sense here used *), or, in 
the language of the hypothetical syllogism, to the modus 
ponensj Our known law is that ' if or wherever M can 
be indicated, §5 is indicated also,' and our application is 
that here, in the case before us (namely S), M can be 
indicated. 

But take next the case where the thesis is an ' Asser- 
tion of Difference,' as S /^ §b : here the word ' sign ' (in 
its ordinary restricted meaning, at least) is far less 
directly applicable. To the deductive argument to prove 

* See pp. 65, 66, 73. 

f Where M is negative (i.e. in the disjunctive argument), this is 
called the modus tollendo ponens. 



Chap. VL] THE EMPLOYMENT OF GUESSWORK- 241 

such a thesis, the name 'Distinction by point of differ- 
ence ' seems better applied : two ' things ' are seen to be 
distinct, since one has, while the other lacks, a certain 
quality. For example : — 

" The release of the Kilmainham prisoners was not a case of • pay- 
ing black mail : ' for now, sir . . . what is paying black mail ? To 
pay black mail is to give something that you would not otherwise 
give. Are we going to do so ? " 

And according as S or § is the possessor of the quality, 
we get two slightly different formulse : — 

(Cesare) S ^ §b : for S — > M, and gj — > non-M : 

(Camestres) S ^ §5 : for S — > non-M, and £5 — > If : 
or, expressed in hypothetical form : — 

(modus ponendo tollens) S /^ Jfe : f° r ^ S were in- 
dicated the absence of M would follow : but here (namely, 
in the case of S) the presence of M is indicated : 

(modus tollens) S /•** ^ : for if §■> w ere indicated, 
the presence of M would follow : but here, the absence, etc. 

And, lastly, take the case where the thesis is symbo- 
lized as S H — > £5,* — the case where (by means of a middle 
term) an exception is brought against some generalisa- 
tion. It is somewhat difficult to frame any single for- 
mula for this mode of argument, while introducing any 
mention of a middle term. But the varieties may be 
reduced to two that appear fundamental, all minor kinds 
being capable of being shown to belong to one or the 
other, f These two are : — 

* The symbol -j-> was explained on p. 68. 

+ For the reduction of these in detail, see Appendix (C). 



242 FALLACIES. [Pabt II. 

(1) S +-> & : for S +-> M, and & — > M (Baroho) : 

(2) S -H> gb : for M +-> gb, and M — > S (Bohardo). 
The distinction made is briefly as follows : the first 

formula includes every case where, in support of a bare 
denial, some point of difference is shown to exist in one 
or more instances between S and £o of the positive 
assertion denied, or where S is shown to possess, in one 
or more instances, a sign (M, or non-M) of the absence of 
Sfe. The second includes every case where an instance, 
or a part of the class spoken of, is brought forward as 
contradicting the generalisation. We may, for conve- 
nience call the former 'Exceptive disproof by Sign 
or Difference/ and the latter ' Exceptive disproof by 
Example.' As instances, we may take for the former : — 

" Quibbling is not necessarily a case of sophistry : for quibbling may 
be unintentional, while sophistry always implies the intention to deceive." 

Or— 

"Honesty is not always the best policy: for honesty sometimes 
means starvation (and what ends in starvation is certainly not, etc.)." 

And for the latter — 

"The radical is not always a man of lofty motives: your mere 
malcontent, for example, is often rather a selfish being, and every mal- 
content is of course a radical." 

Or— 

" It does not follow that a stickler for truth- telling need be narrow 
and severe : quakers, for example, make a great point of telling the 
exact and literal truth, and they are often charitable enough." 

Three main kinds, then, of deductive argument are 
distinguishable : — 
1. Proof by Sign : 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 243 

2. Distinction by Point of Difference : 

3. Exceptive Disproof : 

And it has been noticed that these three apply respec- 
tively to the support of the three different kinds of 
thesis, — S — > 5j, S ^ §j, and S -f— > £?. It seems 
necessary, however, to remove a possible misconstruction 
here. It must not be supposed that Barbara and Celarent 
are themselves never used in Disproof, or Cesare and 
Camestres never used in Proof. On the contrary, both 
Disproof by sign, and Proof by essential difference are 
possible. Thus we might appeal to the sign that 'his 
hat is hanging on its peg,' in disproof of the assertion 
'he has gone into the city;' or, on the other hand, we 
might prove, by means of a point of essential difference, 
the positive assertion that between whales and fishes a 
useful distinction may be made. But since on the whole 
the formula Barbara (or Celarent) is more often used to 
support a positive assertion, while the argument from 
Difference is more often used to support a bare denial of 
analogy or of superficial classification, it seems better, in 
treating the special arguments broadly and typically, to 
connect the former with Proof, the latter with Disproof. 
And as regards the assertion S -f— > Jo, although from 
our point -of view this may be treated as purely negative, 
yet it is undeniable that the vague and flimsy positive 
assertion which such propositions are on occasion used to 
express, may also be supported by the same evidence as 
that employed to support their meaning of bare but 
downright denial. This verbal difficulty need not, I 



24i FALLACIES. [Part II. 

hope, after what has been already said about the inter- 
pretation of grammatical forms, occasion a real stum- 
bling-block. And we may now, before speaking of the 
dangers of deduction as a whole, briefly discuss the 
occasions and purposes for which each of its three 
typical forms is most commonly employed. 

(a) Proof by Sign. 

In one sense, of course, all attempted Proof is an 
attempt to show signs. The Reason itself is always 
given as a supposed sign that the Thesis is true. But as 
contrasted with Empirical Proof, there need be no danger 
in restricting the name of ' Proof by Sign ' to the cases 
where the sign given is plainly recognised as being such 
in general ; where, that is, a middle term is in some way 
referred to, and where accordingly the attempted Proof 
approaches the deductive type. The distinction between 
empirical and deductive proof lies, as already said, in the 
fact that in the latter the proposition stating the universal 
trustworthiness of the sign asserted has already taken 
more definite shape in the mind of the person using the 
argument. Where, as in empirical proof, we argue that 
a theory is true because it is the 'best explanation' of 
certain facts, the proposition summing up the grounds 
on which this is taken to be the best explanation is 
nearly always too complicated to admit of statement 
without much preliminary labour, if at all. But so far 
as we refer to a sign, with definite consciousness that it 



Chap. VL] THE EMPLOYMENT OF GUESSWORK. . 245 

is (in general) a sign of the §?, so far the argument is 
deductive. 

The employment of Proof by Sign is one of the chief 
purposes, and clearly the directest purpose, for which 
every abstract proposition exists. In every abstract pro- 
position, something is said universally to indicate (to be 
a sign of) §fc. And that 'something' becomes thereby 
capable of being made the middle term in Proof by Sign. 
If, therefore, any S can be identified with (or shown to 
indicate) such M, it indicates also, of necessity, that 
which the sign signifies ; for nota notse est nota rei ipsiits. 

In a former chapter * we saw that general names 
might be viewed as labels attached to the ' things ' that 
bear them, and in Proof by Sign we have the clearest 
instance of the operation of the naming process. What- 
ever facts, positive and negative, are included in the 
meaning of a name, are true, of course, of anything 
which rightfully deserves the name. Hence, in order 
to prove one of such facts about a given S, we need 
only show its rightful possession of that particular label. 
While, then, this mode of Proof sometimes proceeds by 
stating both Principle and Application (full Demonstra- 
tion), and sometimes by stating the Principle only, the 
commonest form is where the Eeason states that S de- 
serves (or, for the disjunctive argument, does not deserve) 
the name of M. 

Proof by Sign is, in fact, so familiar and so funda- 
mental a process that it seems hardly worth while to 

* See p. 109, above. 
12 



246 FALLACIES. [Part II. 

spend more time in merely describing it. The dangers 
to which it is liable are our real concern, and these will 
be spoken of presently. But the other two modes of 
deductive argument call for a few words of further 
description. 

(6) Distinction by Point of Difference. 

The exact point of difference between S and §^ is 
sometimes just as dimly conceived as is the resemblance 
relied upon in the Argument by Analogy. As the reader 
may have often noticed, the same class of minds that 
are satisfied with viewing S as ' exactly like ' J&, will 
also be satisfied on occasion (and equally through ab- 
sence of discriminative power) to view them as ' totally 
distinct.' To discriminate is to see points of difference, 
not merely to deny at large all resemblance whatever. 
For some reason, however, the argument from 'indis- 
criminate difference ' has obtained for itself no express 
recognition, though it certainly exists. Possibly this is 
to be explained by the greater pleasure which the view 
of resemblance gives, and thence the greater frequency 
of loose analogy. But since the danger here is essen- 
tially the same as the danger of Analogy, — namely the 
absence of exact discrimination, — there seems to be 
nothing further to say about it as a special kind of 
argument. The remedy is, to call for the supposed point 
of essential difference, and thus to raise the argument to 
the deductive rank. 



Chap. VI.] THE EMPLOYMENT OF GUESSWOKK. 247 

Next, the expression ' essential difference ' is one of 
those which have passed so freely into popular use as to 
be often employed without a clear apprehension of their 
meaning. Essential means again here, essential for some 
purpose understood. And the purpose of essential differ- 
ence always is, to break down some supposed analogy, 
or to deny that S rightly deserves some name. Hence 
it is chiefly for Disproof that Distinction by point of 
difference is used. 

It is clear, however, that any point of difference, essen- 
tial or not, so long as it is thoroughgoing, — so long, that 
is, as S and §b entirely differ in regard to its possession, 
one (universally) having it and the other (universally) 
having it not, — is sufficient to support the thesis S ^ §5. 
But S may differ from £ i n many points, and yet a given 
analogy between them hold good. The whole force of 
this argument, when used in Disproof of analogy or sign, 
depends upon the question whether the point of differ- 
ence (M) is essential for the purpose in hand. 

Those who have not fully grasped the meaning and 
importance of the doctrine as to the burden of proof, 
may find at first sight a difficulty here. Is it incumbent 
on the disputer of an analogy to prove that the difference 
(M) is essential, or must the believer prove the essen- 
tiality of the resemblance relied upon ? The simple 
answer is, that whichever asserts essentiality, whether of 
resemblance or of difference, must prove it or else be 
content to make an apparently unfounded assertion. It 
is, of course, possible that the disputer of an analogy 



248 FALLACIES. [Part II 

may commit himself so far as to say boldly that the 
analogy fails essentially ; but this would be a highly 
gratuitous — often a rash — proceeding on his part. He 
may usefully make a milder assertion about it, namely 
that he sees a point of difference and is anxious to inquire 
whether the believer, having duly taken it into account, 
has reason to suppose it unessential. In that case, of 
course, he avoids all burden of proving anything but 
simple difference, leaving it to the other side to show 
wherein essentiality consists. If, however, — as it is 
sometimes safe to do, — he risks the full assertion that 
the given analogy does fail essentially, let us see what 
it becomes incumbent on him to prove. The analogical 
argument attacked is, say : — 

S — ^ Z : for g, — ^ Z : 
But, says the objector, " ^ — > M, while S — > non-M, 
and M is essential." He asserts then that it is only 
because §•> — > M that §5 — > % I that where M is 
absent the supposed indication of Z is worthless. This 
assertion, therefore, is implied in calling the difference 
essential, and must be proved, like any other assertion, 
before the case is made out. 

From these considerations it follows that Distinction 
by Essential Difference can never be used except in 
Disproof, since the ' essential ' always refers to some- 
thing gone before. And it is also clear that Distinction 
by Simple Difference can rarely be used except with 
reference to some supposed mistake, since the positive 
assertion contained in saying merely that two things 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 249 

differ is so safe as to be practically trivial. Everything 
differs from everything else in some points, — even a coin 
from its neighbour struck the next moment from the 
Mint, — -just as everything also resembles in some point 
(even if it be only in being 'nameable') every other 
thing, The real value of a given assertion of difference 
is to contradict some supposed exaggeration of the im- 
portance due to a superficial or ' striking ' likeness. 



(c) Exceptive Disproof. 

That the exception proves the rule, has passed into 
a popular saying. It is by seeing exceptions, and thus 
guarding our statements, that we establish any law on 
a firm basis, making it henceforward unexceptionable. 
By searching for exceptions we test, or try, the law set 
up for Proof I am aware that this much-abused pro- 
verb is also sometimes interpreted to mean that since 
the given fact deserves to be called an exception it must 
be comparatively rare ; but such an employment of the 
phrase (apart from its etymological shortcomings) borders 
so nearly on the Petitio principii — having no practical 
value except as a somewhat epigrammatic argumentum 
ad hominem, and being often in fact employed for a 
very different purpose — that it seems best to keep in 
view the other and more fruitful meaning. A supposed 
law which is found false in one instance becomes thereby 
fallible in all, until the exceptions are incorporated into 
its statement and thus its application narrowed. Hence 



250 FALLACIES. [Part II. 

Disproof by exception is one of the most important 
processes of verifying, and so establishing or discarding, 
our theories. The ' best explanation/ or ' proved theory/ 
is that which remains over as a residue when all possible 
holes have been picked in the crude or sweeping assertion 
first put forward as a guess. 

Exceptive Disproof is therefore the most frequent 
mode of attacking a generalisation directly: attacking, 
that is, the law itself asserted, not its grounds. To 
attack its grounds, as will be shown presently, the 
best way is either to point out essential difference be- 
tween the cases observed and those inferred, or else to 
point out simple difference and inquire whether or no it 
is known, or why it is judged, to be unessential. But 
exceptive disproof finds at once the contradictory instance. 

Amongst the misleading statements that float about 
so freely in common parlance is one to the effect that 
" Nothing is so hard as to prove a negative." The re- 
verse is the actual case. Disproof, qua Disproof, is safer 
and easier than Proof, just as destruction is less trouble- 
some than construction, In Disproof, since the Thesis 
is a bare denial, we commit ourselves to the least 
possible amount of dogmatic statement. We merely 
assert that some other given proposition is false, with- 
out venturing to say exactly what is true in place of 
it. The fact that underlies, and (with proper explana- 
tion) may be held to justify, the popular expression 
above quoted, is mainly the difficulty that attaches to 
such far-reaching words as 'never/ 'nowhere/ 'no 



Chap. VI.] THE EMPLOYMENT OF GUESSWOEK. 251 

one/ and the like. ' Positive • assertions, whose cor- 
responding negatives are obliged to employ these 
words, are, through their vagueness, so securely guarded 
against being brought to an actual test, that Dis- 
proof often becomes practically impossible. To prove, 
e.g. that my neighbour has never been in New York, or 
that no one has ever held a certain opinion, is of course 
to disprove the very vague assertion that these events 
may (at some time or other) have happened, — an asser- 
tion with which it is commonly safer, and perfectly 
harmless, to agree. Again, Disproof is sometimes as 
difficult as Proof — not more so. To disprove the exist- 
ence of Buddha, or of table-rapping spirits, is manifestly 
impossible so long as there is no admitted test to which 
the question can be brought. But, as De Morgan has 
remarked, whenever we set out to prove (in the narrower 
sense) any Thesis, we must be prepared to disprove any 
one or more of an indefinite number of other assertions 
that conflict with it ; while in order to disprove any 
Thesis we need only reduce it to absurdity ; which is 
often possible without our being prepared to prove a 
single positive assertion about the matter. A definite 
theory, whether abstract or concrete, can be disproved 
by * experience ' more easily than it can be proved : for 
in disproof we have only to find some single instance 
which conflicts with the assertion if abstract, some single 
point in which it fails if concrete. It is in fact mainly 
by means of this simpler disproving operation that the 
securest experimental Proof takes place. All testing of 



252 FALLACIES. [Part II. 

a Theory set up is, at bottom, nothing else than a search 
for contradicting facts existing or inferrible. On the 
thoroughness of the search the value of the test depends. 
After a long life of honourable security any theory may 
be in a moment upset, or at least may be found to need 
qualification, by the discovery of a single hidden circum- 
stance : and experimental inquiry in its highest form is 
in reality an attempt to dispose beforehand of all rele- 
vant facts that can by any means be brought to light. 

As regards the two varieties of this form of argument, 
(given on p. 242) not much requires to be said. The use 
of the one or the other clearly depends on the nature of 
our previous knowledge bearing on the question raised. 
Neither mode can, I think, be called altogether safer or 
better than the other, since even direct identification of 
M with S may well be mistaken. If, however, any pre- 
ference is to be given, perhaps the latter (Bokardo) should 
have it. The dangers in the way of these, as of all forms 
of deductive argument, will be treated in a later section. 

III. The Dangers of the Argument by Example* 

(a) The Dangers of Analogy. 

In both kinds of Argument by Example, — Analogical 
reasoning and Inductive Proof — the primary danger is 
that of overlooking some hidden element in the facts, 
and thereby generalising too freely, rather than that 

* The dangers peculiar to the special types of argument are shown, 
all together, in a table (V.) in the Appendix (E). 



Chap. VI.] THE EMPLOYMENT OF GUESSWOKK. 253 

of accepting a definite principle which, true or not, 
does not apply. We are not here concerned with any 
dangers to argument when the principle relied upon is 
simple and clear, but solely with those incident to rapid 
unconscious employment of some highly complicated 
principle, or to our hurried summary of the total outcome 
of a conflict between unnumbered dimly formulated laws. 

It was said above that in adopting Mill's formula for 
Analogy as typical, we must bear in mind that an actual 
argument, though truly analogical, may easily appear on 
the surface not quite to fit the formula. But this formula 
is nevertheless a perfectly legitimate simplification, since 
it serves to generalise the one danger to which all analo- 
gical arguments, in so far as analogical, are primarily 
liable : the danger, namely, that the resemblance between 
the cases supposed to be analogous is only a superficial 
one, — or, more widely still, that the resemblance, even 
if on the whole real and deep, is not essential for the 
purpose intended. So far as an argument professes to 
rest on analogy, the matter of first importance is to ascer- 
tain, if possible, the exact points of resemblance and 
difference between the cases compared, and to inquire 
further whether the resemblance as thus defined and 
limited has any right to be considered essential in regard 
to the purpose for which it is in the given case employed. 

We saw also that the real difficulty in clearly placing 
the argument from Analogy among special kinds of 
Proof, arises from the fact that as soon as the exact 
points of resemblance relied upon come into clear view 



254» FALLACIES. [Part II. 

the argument ceases to be analogical, and becomes deduc- 
tive. That is to say, if we rest our belief that S — > Z 
on the observed fact that £fc> (which resembles S in the 
point M) — > Z, we are really beginning to employ, 
instead of mere analogy, the full syllogism ' S — > Z, for 
S — > M, and M * — > Z.' Our clear recognition, that 
is, of the exact extent of resemblance relied upon, is 
itself a recognition of the underlying Principle by virtue 
of Which S and ^ are considered ' parallel cases ; * in 
other words, is an assumption of a Law from which our 
thesis may be deduced. Take, for instance, the argument 
sometimes employed against Sunday closing, that since 
the upper classes have their clubs open on that day it 
would be unfair to deprive the poor of their only places 
of resort and refreshment. It is clear at once that we 
have here a case of complicated or double analogy, clubs 
being considered to ' essentially resemble ' public-houses, 
and the upper classes to essentially resemble the lower. 
But what is meant by ' essential resemblance ? ' Not, 
surely, that the things compared are precisely alike in all 
respects, — else detection of false analogy would be a far 
simpler matter than at present but that for the purposes 
immediately in view, the points of difference may be 
neglected. Now, as soon as we begin to neglect points of 
difference, no matter where, we begin to generalise : that 
is to say, we extend the possible range of our assertion. 
That which constitutes individuality is always the 
difference (i.e. peculiarity) that an individual possesses 

* If not universally, at any rate equally when limited by S and <&. 



Chap. VI] THE EMPLOYMENT OF GUESSWORK. 255 

over and above any class to which he may belong, 
just as we have seen* that it is differentia that 
the sub-class or species possesses over and above the 
genus, So far, then, as we neglect the points of difference 
between clubs and public-houses, or between one class of 
men and another, we speak of them no longer as distinct 
individual things, but as members of some wider class * 
which includes them and may possibly include other 
things as well. In the instance quoted, the key to the 
class intended is expressly given in the case of the 
analogy between clubs and public-houses : it is the being 
places of 'resort and refreshment' that is considered 
essential : this is the point of resemblance in virtue of 
which (i.e. to the extent of which) what is true of the 
one is supposed to be true of the other. As regards the 
analogy between upper and lower classes, it seems to 
have been thought unnecessary, or unsafe, to give the 
key expressly; such maxims as that "no class in the 
State should be specially favoured without reason shown n 
being widely accepted as a basis of legislation. And if 
this account of the analogy intended be a correct one, — 
if it is only as being places of resort and refreshment 
that public-houses are to be kept open for the benefit of 
the poor in their sole capacity of citizens of the State 
(or whatever may be the wide class to which upper and 
lower classes equally belong) — then we thereby imply 
the Generalisation, or Law, or Principle, "All citizens 
of the State are (a- priori) equally entitled to their 

* <?/. p. 108, above. 



256 FALLACIES. [Part II. 

places of resort and refreshment ; " by means of which, if 
true, the Thesis may be deductively proved. 

However important, therefore, Analogy may be as 
setting us on the track of a fruitful Inference, as a mode 
of Proof it is in itself almost wholly worthless, — only 
sufficient, that is, to raise a vague and slight presumption 
where no better evidence can be obtained. It is perhaps 
more widely applied, in common discourse, even for 
Proof as well as for Inference, than any other form of 
argument. But this seems to be chiefly due to the slack- 
ness with which our examination of evidence is commonly 
carried on. It is so much less trouble to see that two 
things bear a ' striking resemblance ' than to discriminate 
accurately how far the resemblance really goes, and the 
points wherein they differ. There is nothing, pro- 
bably, that is more characteristic of the higher* in- 
tellect as contrasted with the lower than its greater 
power of discriminating, — i.e. of seeing points of differ- 
ence. It is differentiation that is always the law of 
progress. Knowledge begins as a vague blur, which 
gradually becomes distinct Everywhere the specialist's 
eye sees finer shades of difference than are visible to the 
public, — as the shepherd knows his sheep. It is incapa- 
city for seeing difference that lies at the root of all crude, 
ill-considered generalisation, and therefore at the root of 
the mental ' narrowness ' (as it is usually called) which is 

* C/. H. Spencer, Psychology, p. 220. " Incident forces that seem 
alike to a loAvly endowed creature, seem conspicuously unlike to a crea- 
ture endowed with the sense-organs required for appreciating them." 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 257 

ever ready to accept a principle unduly simple and wide 
in its asserted sweep, and therefore unduly rigid in its 
actual application. It is neglect of difference that always 
marks the ruder nature, easily content with the roughest 
weights and measures. It is the besetting danger not 
only of ignorance as opposed to experience, of clumsiness 
as opposed to delicacy of touch, but also of the habit 
of dreamy theorising as opposed to patient reverence for 
fact. 

In thus noticing the harm of neglecting difference, I 
must not be understood, of course, to advocate the neg- 
lect of real resemblance ; only to say that this is a fault 
to which the majority are in practice far less liable. The 
inducements to over-generalise are on the whole stronger 
than those to indulge in excessive hair-splitting. And 
apart from mere ignorance or incapacity, it is always less 
trouble to avoid distinguishing, even when we have 
attained the power : the recognition of resemblance, 
whether justified or not, is always a more pleasant 
operation, simplifying Nature and thereby giving freedom, 
and also much self-satisfaction, to the mind that sees the 
supposed analogy. Hence, no doubt, much of the charm 
of metaphor and of the cruder kinds of poetry, and 
hence the efficacy, in spite of its unfairness, of caricature. 
Whatever appeals to our idleness, while at the same time 
gently flattering our sense of ' breadth of view,' always 
bids fair to win a wide reception. In its effects, hair- 
splitting is perhaps a more deadly fault than coarseness 
of vision, though less the property of the uninstructed, the 



258 FALLACIES. [Part II. 

thoughtless, the impatient, and the clumsy. The power 
of seeing differences, exclusively cultivated, leads no doubt 
to a casuistry and a hesitation which are far from being 
either pleasant or practical. So, too, the mere neglect of 
resemblance, without at the same time a distinct and 
conscious vision of differences, cripples our power of ex- 
tended sight and of useful generalisation. This forms 
indeed no fallacy, as the term is generally understood ; 
but it is a serious limitation, as the existence and spread 
of general names, and of science itself, bears standing 
witness. Often, no doubt, it is merely the recoil from 
hasty generalisation that leads to the adoption of ' rule 
of thumb : ' in any case, however, this is of course a 
falling short from the ideal. 

It is the undue neglect of difference, then, in the midst 
of recognised resemblance, that constitutes the fallacy of 
False Analogy, just as the due neglect of difference con- 
stitutes sound generalisation. While the ideal is, to give 
to both Resemblance and Difference their due weight, the 
actual course of the history of knowledge, so far back as 
it can be traced, is a record mainly of unsuspected dif- 
ferences brought to light. Where any sound generalisa- 
tion has been reached, it has in most cases either been 
preceded by deep analysis, or is itself the residue of an 
unsound generalisation after it has gone through a pro- 
cess of limitation and restriction in order to make it fit 
the facts. Further back than any records go, Philology 
helps us to see that the earliest traceable formation of 
language has proceeded also by analysis of what first 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 259 

seemed simple. First we find one word employed for 
what we now know to be many different things : gradu- 
ally, as insight deepens, new words grow up, in order to 
mark off groups and portions as distinct. While there 
may be a synthesis based upon analysis, the first step is 
to analyse what before seemed simple. 

The shapes in which False Analogy usually occurs are 
very numerous. They range from open reliance on 
Analogy in lieu of Proof, down to the finest shades of 
rhetorical suggestion by means of metaphor ; and even 
into the region where metaphor ceases to be distinguish- 
able as such, and where we reach the unavoidable short- 
comings of language. Taking first the more definite end 
of the scale, the following example will show to some 
extent the dangers of analogy. An eminent author, 
writing on the work of the English Church before the 
Tractarian movement, contrasts the newer state of things 
unfavourably with the older, because the Church in those 
former days 

" taught us to use religion as a light by which to see our way 
along the road of duty. Without the Sun our eyes would be of no use 
to us ; but if we look at the San we are simply dazzled and can see 
neither it nor anything else. It is precisely the same with theological 
speculations. If the beacon lamp is shining a man of healthy mind 
will not discuss the composition of the flame." 

Here, of course, the resemblance between the Pro- 
testant religion and a light to lighten the road of 
duty is sufficiently striking, and (if it be granted, as 
for the purpose of this argument it may safely be, 



260 FALLACIES. [Part II. 

that the light is no mere will-of-the-wisp) no fault 
need be found with the metaphor so far. But in what 
respects do ' theological speculations ' really resemble 
the process of ' looking at the light ' ? Whatever 
other faults the movement spoken of may have had, 
surely it was, in essentials, an attempt to look more 
closely at the road of duty as illumined by the light. To 
call this looking at the light is merely a loose and con- 
venient elliptical expression. At any rate, nothing is 
openly said by the writer to show that this latter 
employment of the metaphor is not a better one, and if 
we are to suppose such a denial covertly made, it comes 
very near to begging the most important question con- 
cerned. But in order to show more strikingly the 
worthless character of analogy as argument, it may be 
further noticed that in the second half of the sentence 
the metaphor is changed, by its author himself, in a way 
that saves an opponent all trouble, inasmuch as it forces 
the first analogy to defeat its own purpose. Religion 
becomes no longer a Sun for lighting up the road, but 
a 'beacon lamp,' — a thing whose use and purpose is 
precisely to be looked at : and in order to save the argu- 
ment, theological speculation has now to be likened to 
'discussing the composition of the flame.' Would not 
the Tractarians say rather that if they cared to discuss 
the composition of the flame at all, it was only so far as 
might enable them to be sure that this really was the 
' beacon lamp ' of which they were in search ? Analogy 
used in this way is, no doubt, as things are, a powerful 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 261 

rhetorical instrument ; but it is not one that is destined 
to extend its influence in the future. The remedy is so 
easy. Give a dealer in analogy rope enough and he will 
probably end as above ; but if not, and if it be considered 
too much trouble, or too difficult, or too slow, to inquire 
exactly into the real points of resemblance and difference, 
nothing is simpler than to change the metaphor and so turn 
the tables. One arguer can always assert covertly as well 
as another, and it requires no great intellectual strain to 
produce a happy simile or to fix the attention of a busy 
or thoughtless audience on some ' striking likeness ' which 
is so neat and pretty that it seems to them it cannot 
be untrue. It is, however, solely when a supposed 
analogy is put (or accepted) in place of argument that 
harm is done. As mere illustration, or as re-assertion 
of a thesis in a more concrete form, only pedantry can 
object to it ; and as supplying the first vague hints for 
future verification it will always be the chief stepping- 
stone to good results. But the line between employing 
Analogy as argument and employing it with an open 
recognition of its dangers is so exceedingly fine that it 
becomes in practice almost impossible to over-estimate the 
need of keeping a jealous guard against neglected points 
of difference. It must also be remarked, that even where 
the analogy is plainly a false one, it is always possible 
that the person employing it has himself been under no 
delusion as to the gap requiring to be filled up, but has 
only overrated the discriminative power of his audience, 
— or forgotten their readiness to be deceived. 



262 FALLACIES. [Part II. 

Open reliance on Analogy as argument is rare. The 
analogical arguments that we find actually employed 
show a decided disinclination to express themselves in a 
quite straightforward fashion ; unless, indeed, as in some 
of the cases above quoted, the connecting link (or middle 
term) is fairly obvious, and the argument, therefore, 
already nearly deductive and easily raised to that higher 
rank. As a general rule, the more merely analogical (i.e. 
the less deductive) the argument is, the more will it 
naturally tend to avoid open and definite expression by 
means of this simplest formula : for the definite expres- 
sion of reliance upon the resemblance between S and §j 
to prove a definite assertion regarding S, is apt to pave 
the way for inquiries that are then felt to be awkward. 
When the Analogy is a weak one (and equally when the 
points of resemblance are numerous or not easily 
summed up) nothing of course is more damping to the 
argument than any call for a clear statement of the exact 
points of resemblance relied upon ; and hence in many 
cases even the setting S and §•> clearly side by side, and 
reducing the reasoning to the above formula, becomes 
almost tantamount to a reduction of the whole argument 
to absurdity ; and is constantly employed for that purpose. 
Thus when a speaker in Parliament declared that — 

" To say that there was nothing in the nature of a compact or 
agreement between the Government and the gentlemen whom they 
had been keeping in confinement without trial, reminded him of the 
principal character in one of Moliere's comedies, who said that he had 
not sold anything, but had merely given it away to his friends and 
they had given him some money in exchange — " 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 263 

we find the other side making answer that — 

" So far as the speech of the hon. member was not a mere baseless 
dream ... it contains at least this one statement, that because in 
Molierc there was a man who, having sold goods and received a price, 
pretended that he had made a present of the goods and received a pre- 
sent in return, the position of the Government is analogous to that 
man." 

And then comes a statement of the " essential differ- 
ence " between the two apparently parallel cases. 

As a general rule, then, Analogy has a tendency in 
practice to put itself forward either as merely intended 
to raise a vague presumption, or else (and more com- 
monly), with an air of coming ex abundanti, rather than 
as being in fact the sole evidence relied upon. It is 
usually given, however unintentionally, in such a manner 
that, if objections should be raised, it remains easy to 
claim that only an illustration was intended, and to grant 
with much candour that possibly as an illustration it 
fails to fit the case exactly; a process which closely 
resembles the parliamentary practice of first using and 
then ' withdrawing ' an offensive expression. The express 
words ' because/ or ' for,' or ' since,' are as a rule 
omitted by the speaker: the connexion will be amply 
supplied, as every experienced rhetorician must know, by 
any average audience, and being thus voluntarily supplied 
by the audience, will probably be less exposed to their 
criticism. Whately, for example, did not write, "In- 
ductive Logic can never be a rival to the Aristotelian 
Logic, since a plough can never be substituted for a flail," 
but he wrote that Inductive Logic — 



204 FALLACIES. [Part II. 

" Would not . . . have the same object proposed with the Aristo- 
telian Logic ; nor be in any respect a rival to that system. A plough 
may be a much more ingenious and valuable instrument than a flail, 
but it can never be substituted for it." * 

Or again, Sir S. Northcote (speaking at Balham), 

did not say "Mr. Gladstone, because he is fond of 

hewing down trees, will be likely to want to hew down 

our institutions," but he said — 

" We shall be abused by a great number of people because we 
hesitate to give to the Prime Minister exactly the facilities he de- 
mands, but we shall endeavour to do our duty when those demands 
are made upon us ; and we may take to heart one of those wise fables 
on which our youth was nourished. You may remember how a cer- 
tain woodman went into the forest and asked the trees to lend him a 
bit of wood in order that he might make a handle to his axe. When 
they were unwise enough to give him a piece of wood, you recollect 
what happened to the trees themselves by the use the woodman made 
of the axe (cheers and laughter)." * 

These examples will be sufficient to show what is here 
intended. But the difficulty of deciding whether the 
Analogy was really relied upon as evidence, or genuinely 
and legitimately put forward as an illustration merely, 
or to point a quaint and semi-serious fancy, is not the 
only one to which we are exposed in practice, nor the 
most perplexing. This can, indeed, to a great extent be 
met (much as an unparliamentary expression may be 
met) by demanding a disclaimer on the spot. A far more 
difficult question arises when we attempt to fix the line 
between the metaphorical and the direct use of names 

* The reader will notice that these cases are not given as examples 
of false analogy, but merely of the usual method of getting an analogy 
(true or false) accepted by an audience. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 265 

And perhaps the most frequent manner in which covert 
analogy is used as argument, is by condensation into a 
name which just escapes being considered far-fetched or 
metaphorical. 

" It was observed by a sound thinker in those parts, that property- 
was ballast, and when once the aptness of that metaphor had been 
perceived, it followed that a man was not fit to navigate the sea of 
politics without a great deal of such ballast." 

That which to George Eliot and to most of her readers 
was clearly a mere metaphor, the aptness of which 
was all-important to the force of the argument, passed 
easily, she tells us, among the less educated electors 
of Treby Magna, as hardly distinguishable from a plain 
statement of fact. The power of recognising metaphor 
as metaphor is one of the latest and highest acquisitions 
(so far as it is yet acquired) of mankind ; an outgrowth 
of the accurate spirit which marks off modern science 
from the ancient reign of florid imagination. 

To some extent, however, we are all in the position of 
these electors. We smile at their simplicity, but future 
generations will smile at ours in turn. The schoolboy 
of the twentieth century may find a difficulty in realising 
that his ancestors were misled into supposing fleshiness 
of body to be "padding against the shafts of disease," 
or a glass of sherry taken just after a large and varied 
dinner, to be, in the sense intended, a "whitewash." 
At present the words are few where metaphor is wholly 
absent, and under metaphor wherever employed some 
danger lurks. Who is to guarantee, for example, that 



266 FALLACIES. [Part II. 

the expression that danger "lurks" in metaphor will 
not at all mislead us ? We are always rather prone to 
personify abstractions, and so far as we really picture 
Fallacy as external to ourselves, we are neglecting one 
of the most important facts about it. 

Proverbs again are frequently employed in arguing by 
indistinct resemblance. It is the slackness with which 
any ' striking ' analogy will commonly pass muster that 
leads at all times to the use so freely made of proverbs. 
To assume that some case comes under some well-known 
proverb, without a shadow of evidence to show that it 
does so beyond what may be gathered from the crudest 
superficial inspection, is still in many quarters a favourite 
practice. Hence, as a rule, the earliest recorded crys- 
tallisation of wisdom has usually been a collection of 
proverbs or of fables or allegories, — which latter are 
only a less generalised form of the same expedient, — and 
to some extent the process appears to be still going on. 
It is true that in these times such oracular wisdom 
obtains less influence than in the days of Solomon or 
even of Bacon, but one must admit that there is still 
some chance for a writer to win in this way a certain 
popular reputation for prophetic insight. On all such 
easy dogmatism the action of Logic is apt to be purely 
repressive. 

We see then, in short, that analogical reasoning may 
be defined as the dim and unsupported assertion of 
essential resemblance. To assert essential resemblance 
is in itself a large undertaking, and yet there are few 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 267 

assertions which are commonly made with a lighter 
heart or believed more obstinately. Only before the 
resemblance between S and Jfc is clearly defined and 
limited, can an argument be properly called analogical : 
and meeting with an argument which is at present in the 
merely analogical stage, the first step towards its exami- 
nation is the attempt to clearly define and limit the 
extent of the resemblance and difference supposed to 
exist : which attempt, so far as successful, destroys the 
merely analogical character of the argument, by bring- 
ing into daylight the supposed underlying Principle. 
The special danger of any argument, so far as it relies 
upon Analogy, is the possible existence of unsuspected 
and essential difference between the things compared. 
This is the vital point of every analogical argument, the 
point to which attack should be directed, and which, if 
we are defending the analogy, it behoves us most to be 
prepared to guard. Until this doubt is set at rest, there 
is nothing to show that the resemblance, how striking 
soever, is more than surface-deep, or, even if really far- 
reaching, that it has any bearing upon the special point 
at issue. 

(6) The Dangers of Induction. 
Before beginning to discuss the dangers of the induc- 
tive mode of argument, it may be worth while to recall 
attention to the various shades of assertion comprised 
under the extremely general formula S — > §j. In the 
first place, it must be remembered (as noticed at pp. 78-83) 



268 FALLACIES. [Part II. 

that at the present stage of knowledge the propositions 
where such a statement can be in practice interpreted 
quite unreservedly are comparatively few in number. 
Here and there, certainly, we have discovered generalisa- 
tions which seem absolutely true, so far at least as our tests 
can yet try them and so far as all present practical pur- 
poses are concerned, — such as the Law of Causation itself, 
or the law that human beings have human ancestors, 
or that all matter gravitates, or that decapitation causes 
death. But for the most part, even in Science, we are 
forced to be content with laws which express tendencies * 
merely. Often, indeed, we think ourselves fortunate if 
we can reach any shadow of a law at all. It is no ex- 
aggeration to say that the greater part of the knowledge 
on which daily conduct depends for its rationalisation 
consists solely of generalisations which, however crudely 
and boldly expressed and at intervals believed, are really 
apprehended (so far as regards persistent or fruitful 
apprehension) in the dimmest and vaguest way. To go 
no further than the popular maxim in favour of speaking 
the truth, every thoughtful person will admit nowadays 
that the law as usually stated needs some qualification ; 
although most people feel the admission dangerous, since 
no one has yet been able to formulate the real law so 
as, while avoiding mere platitude, to take in all the 
exceptions. 

* The law of Gravity, it should he noticed, merely avoids this diffi- 
culty in a verbal manner. It is absolutely true that all matter gravitates : 
but 'gravitates' is a word coined to express the meaning 'tends to 
fall.' 



Chap. VL] THE EMPLOYMENT OF GUESSWORK. 269 

Next, S (in general) may be asserted to indicate J& 
(whether absolutely or reservedly) either as its cause, its 
concomitant, or its effect, — that is, either as having ex- 
isted, as existing, or as to exist in the future. To assert 
that ^ is * the sole cause of S is to assert absolutely that 
S wherever found indicates Jo's past existence {e.g. ' Life 
is always due to prior life ') : to assert the same indica- 
tion ' reservedly ' is to assert either that §j is one cause 
but that there may be others ; or, in the most reserved 
form of all, that an observed sequence ^ followed by S 
was ' not purely accidental.' f To assert absolutely that 
S wherever found indicates §j's present existence, is to 
assert that every S without exception possesses the 
attribute, belongs to the class, deserves the name, or is 
found in conjunction with, §^ : to assert the same re- 
servedly is to assert that S and §■> are more or less often 
found together (or that S is nearly always, usually, 
frequently, jk) — more often than mere coincidence will 
account for, -or again that the observed conjunction S 
and £o i n co-existence will at least tend to recur. To 
assert absolutely that S wherever found indicates g^'s 
future existence is to assert not only that S is a cause 
(or the cause) of £&, but that no other cause is ever 
capable of interfering with it, — a very large assertion : to 
assert the same reservedly is to assert that S, unless 
something unspecified interferes, may serve as a sign that 

* To say that J5 teas the sole cause generally bears a quite different 
meaning, namely that some other thing (perhaps vaguely specified) was 
not operative. 

t See note at p. 81. 
13 



270 FALLACIES. [Part II. 

£b will happen, or that the observed sequence S followed 
by £b will tend to recur. 

In spite of these tangled variations there is, as it 
seems to me, a sufficient reason for framing the formula 
as above. This is the ideal type, by comparison with 
which any actual shortcomings may best be made 
apparent. If S does not indicate §•> quite absolutely, 
there is no better means of seeing why and how far it 
falls short of doing so, than an inquiry what are the 
dangers to which such certainty is exposed and what 
has been done to guard against them. And as for the 
time-element, that may be neglected, so far as a first out- 
lined view of the dangers is concerned* Just as the 
process may be generalised, so may the dangers. In 
spite of their surface variations their deepest meaning is 
the same. There is at bottom one primary source of 
fallacy in the inductive argument, call it by whatever 
name may be most convenient. We may name it, for 
instance, the danger of " overlooking Plurality of Causes, 
or neglecting possible Chance or Counteraction," or " the 
possibility of unknown antecedents," or " arguing either 
post hoc ergo propter hoc or per enumerationem simpli- 
cem" or " neglecting to exclude alternative possibilities," 
or " forgetting that facts may bear more than one inter- 
pretation," or " stating the law too widely," or " failing 
to see below the surface," or — perhaps on the whole best 
of all — " unduly neglecting points of difference." 

It may be well here to make a slight digression in 
order to show more definitely how ' undue neglect of dif- 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 271 

ference ' is the main danger of direct generalisation just 
as of the argument from analogy. Concrete evidence for 
an abstract law consists, it has been said, of a case or cases 
brought forward, of which such law is asserted to be the 
best explanation. If then some better explanation is 
possible the theory as stated is impeachable. But what 
is meant by a better explanation ? Can there be degrees 
of explanation, so long as the facts are all explained ? 
Surely the facts relied upon either do or do not all form 
cases under the law asserted ? Surely the term ' better ' 
or ' worse ' is inappropriate ? By the best explanation is 
meant, however, not only any law from which all the 
facts observed are deducible, — for we may often frame 
many different hypotheses, inconsistent with each other, 
which will each explain all the facts ; but what is meant 
is, that solitary one out of all possible hypotheses which, 
while explaining all the facts already in view, is 
narrowed, limited, hedged, or qualified, sufficiently to 
guard in the best possible way against undiscovered ex- 
ceptions also. The wider the law the greater the danger, 
until precautions are taken : and it is in the strength of 
these precautions that the value of any Theory lies. It 
is a merely negative condition, or absolute sine qua non, 
that a Theory shall at least explain the facts already in 
view: failing this, it is condemned, or seen to need 
qualification, on the threshold. But bej^ond and above 
the preliminary condition that no known fact as yet con- 
tradicts the theory, we need also the assurance, in some 
shape or other, that if there were exceptions (or con- 



272 FALLACIES. [Part IL 

tradictory instances) their existence would already have 
been discovered or inferrible. This assurance it is which 
forms the turning-point of inductive proof. Hence the 
* best ' explanation of the facts A and B and C is that 
explanation which while neglecting certain points of 
difference among them, and thus forming some generalisa- 
tion, neglects only those differences which are 'un- 
essential : ' the best explanation of (i.e. generalisation 
from) one solitary sequence observed is that which 
neglects only its unessential elements or features. While 
all generalisation exists by neglecting points of difference, 
the soundness of any generalisation consists entirely in 
the completeness with which it balances out the relative 
importance of the points of difference concerned. The 
assumption at the bottom of all our explanation and pre- 
diction — of all our reduction of Nature to Law — is not 
only that the same antecedents will have the same con- 
sequents (for it seems hardly necessary to say that no 
two total sets of circumstances ever were or will be 
precisely alike *), but that whenever some of the observed 
circumstances recur, some of the same antecedents, con- 
comitants and consequents may be looked for. The 
problem is always to discover exactly which of the com- 
ponent circumstances of one total event are essential to 
any given portion selected from those of another. Every 
abstract proposition selects some only as being essential, 

* Just as the members of every class of objects Lave their points of 
dissimilarity from each other, as well as the points of similarity which 
constitute them a class, so have the members of any class of events. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 273 

and it is through deep analysis of the actual circumstances 
that we avoid selecting too few. The two opposite 
modes of missing the ideal, then, are : — (1) to be content 
with too little repetition of circumstances — too broad a 
law, — as when we say in our haste " All men are liars," 
and (2) to demand too exact a repetition of circumstances 
— too narrow a law, — as in the case of the Chinaman who 
burnt down his house in order to repeat as far as possible 
the exact circumstances in which he first obtained a 
certain kind of cookery. The former fault is the induc- 
tive fallacy proper : the latter may be a serious hindrance 
to knowledge, or may lead to a waste of time or money 
or trouble, but it makes no false pretence and thus runs 
less risk of failure in obtaining the immediate effect 
required. 

It is in every case, then, through undue neglect of the 
essential difference between the specific case or cases 
observed and the wider genus to which the assertion 
professes to refer, that we rise to a generalisation not 
sufficiently guarded against possible exceptions. The 
ideal is, to frame every generalisation unexceptionably, — 
so that no exception can be found, — and this whether 
the outward form that the statement takes is simple — as 
in "All matter gravitates," — or qualified, as in "All 
stones fall to the ground except when restrained in 
certain ways from doing so." It is either by far-reach- 
ing foresight or by growing experience that exceptions 
come to light; and when they are recognised, the 
supposed law has either to be abandoned altogether (if 



274 FALLACIES. [Part IT. 

they are numerous and important) or modified in order 
to take them in. The experimental methods are thus, 
in one aspect, methods for as far as possible anticipating 
the discovery of exceptions. 

The first and weakest remedy against stating as a law 
at all, what should properly be called a coincidence, is 
the employment of the Theory of Probabilities: an 
immense subject, and full of dangers of its own. Any 
full discussion of its details is here out of the question ; * 
nor, indeed, is it required for our purposes. It may, how- 
ever, be explained that, as regards Proof and Disproof — 
i.e. as regards the simple answer Yes or No, to a question 
raised and debated, — the chief operation of the doctrine 
is in enabling us to say in certain cases that S and §b 
(e.g. sun-spots and magnetic storms) occur in conjunc- 
tion more frequently than can be accounted for by mere 
coincidence. In the absence of any knowledge of the 
causation concerned, such a result may, no doubt, have a 
certain value. But in pursuance of our plan, we shall 
confine attention to the more marked and definite end 
of the scale. The employment of the Doctrine of Chances 
must always be superseded by more stringent methods as 
soon as inquiry passes beyond its very earliest and most 
tentative stages. 

Since, then, for complete proof of a law from facts 
two things are necessary : — 

* Mr. Venn's Logic of Chance is generally considered the best 
English work on the subject. See also Mill's Logic, bk. iii. chaps, xvii. 
xviii. and xxiii. ; and Bain's Induction, chap. ix. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 275 

' (1) The assurance that no contradictory instance has 
yet been found, and 

(2) The assurance that if a contradictory instance 
existed its existence would be known : 
it follows that negatively all turns on the finding of con- 
tradictory instances, while positively all turns on the 
completeness of the search for them. All positive proof 
depends not on the fact of observations having been made 
nor even on the fact of experiments having been per- 
formed; but on the care, the precautions, with which 
observation has been interpreted and experiment con- 
ducted. So far only as these exclude alternative 
possibilities, are they of real value. 

We have noticed, more than once, the danger of over- 
looking alternative possibilities. And it is true that 
every Theory set up has, in the first place, to show its 
preferability over all conflicting theories. This is pre- 
cisely what is meant by saying that the burden of proof 
remains. Just because Disproof is easier than Proof,* 
and because all positive assertion can only justify itself 
as a remainder when negative assertions are subtracted — 
when mistakes have been either one by one eliminated 
or in a body prevented — the burden of doubt to be 
removed by evidence consists essentially in the group of 
alternative theories remaining undiscarded. The impor- 
tant point is always, to show that all other possible 
theories are weighed in the balance and found wanting : 
that is to say, that all precautions have been taken against 

• See p. 250. 



276 FALLACIES. [Part II. 

that crudest kind of unchecked generalisation which the 
least trained mind possesses ever in greatest abundance. 

This objection against a theory — that alternative 
theories are not yet discarded — appears, however, more 
directly applicable, more fruitful of results, against a 
concrete or an abstract-concrete thesis than against a 
directly abstract one ; and as a method of attack on such 
theses, where for any reason it may be inconvenient to 
search for the supposed underlying Principles, it could 
no doubt be made useful. Accordingly I have thought 
it worth while to set out in an Appendix (A) a sum- 
mary of the alternative theories amongst which any 
observed concrete sequence or coexistence has to choose. 
Every observation or experiment interpreted is a case of 
the assertion of an abstract-concrete proposition. Find- 
ing S followed or accompanied by £fc, under certain con- 
ditions, we assert causal connection between them. And 
the right of the theory chosen, over all its possible rivals, 
depends entirely upon the depth of our insight into the 
conditions under which the experiment or observation 
was really made. This is the main lesson of Logic, as 
regards Induction. The illogical person is content to 
produce, as evidence for a supposed instance of causation, 
the bare fact of succession in time, or unexplained con- 
comitance, — as, for example, in the case of quack re- 
medies, or again, in nearly all cases of superstitious 
belief; while inductive science always demands as 
full an analysis as possible, of all the circumstances. 
Failing this, as with all care it must sometimes fail, the 
proof is recognised as weak. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 277 

(c) The Empirical Methods. 

Of Empirical Methods the only careful classification 
yet made is, I believe, Mill's well-known list of five. 
While, as their author himself (and more lately, Professor 
Jevons) expended labour in showing, none of these is, 
except in an ideal sense, completely satisfactory as a 
guarantee, but in every case a further assertion is 
practically wanted; yet the statement of the method 
employed in the given experiment or observation, to- 
gether with the precautions taken against its special 
dangers, may be regarded as the answer given to the 
challenge of possible alternatives : in other words, as a 
means of shifting the burden of proof. 

Since there may possibly be, in some quarters, a dis- 
position to take these methods for more than they were 
probably intended to be worth, there will perhaps be some 
use in reminding the reader that it is the guarding 
against the danger to which each method is liable, that 
is in every case the all-important circumstance — far more 
so than the mere employment of this or the other 
method. It is not, for instance, because a given experi- 
ment " proceeds according to the Method of Difference " 
that the evidence is strong, but because by means of 
certain precautions (often more easily taken under the 
Method of Difference than in the other cases) we happen 
to have approximately reached the ideal there set up. 
A careful employment of the " weakest " of the methods 
is often better than a loose employment of the strongest. 



278 FALLACIES. [Part II. 

It seems unnecessary in this place to obscure our 
more general view by entering upon the Empirical 
Methods in detail and discussing their special liabilities 
to frustration.* It will be enough here to remark that 
ultimately the sole danger of fallacy in empirical proof 
is that of neglecting to take into account the differences 
between the Antecedent (or Consequent) observed in 
any actual sequenced and that spoken of in the S (or ffc) 
of our abstract proposition based upon it. In any 
sequence observed in Nature there are usually certain 
elements overlooked at first, and if one of these be 
important, our ' natural ' inference is to that extent 
misguided. Thus for a long time the possibility was 
overlooked that the phenomena of fermentation could be 
due to germs floating in the air. From the most careful 
experiments that were made up to the beginning of the 
present century, the belief was held that since all the 
possible external sources were known and guarded 
against, the generation of the yeast-plant must take 
place in some 'spontaneous' fashion within the fluid 
itself. So again, until quite recently it was commonly 
believed that the carbon of vegetable produce must come 
from the soil : that it should be almost entirely derived 
from colourless air, seemed on the face of it unlikely. 

The same danger may be otherwise phrased by say- 

* I have, however, thought it well to set these out in the Appendix 
(B). 

f For brevity I here speak of sequence only ; since unless causation 
be a dream, co-existence may always be reduced to a complex result of 
sequences. See also Appendix (A). 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 279 

ing that the empirical fallacy consists in resting our 
proof of a law or theory on confirmatory (i.e. congruent) 
facts alone. If the facts around us do not fit our theories 
we have of course unanswerable disproof: but if the 
facts do fit them, the theories are not yet necessarily 
secure. We need besides such facts, in every case the 
further assurance that any contradictory facts, if existing, i 
would have come to light. And so far as this assurance 
is wanting, so far the proof is weak. Mere number of 
confirmatory facts will sometimes yield us this assurance, 
but only so far as in the given case the special circum- 
stances guarantee this, is number of any avail. In many 
cases (e.g. in most chemical experiments) a single instance 
is more trustworthy than a thousand of another kind, 
since here the precautions are often enough to exclude 
c unknown antecedents.' The assurance lies outside any 
inductive methods : for the various methods merely cor- 
respond to various forms which the same difficulty takes 
on. It is analysis only that can enable us to know how 
far we have really reckoned with unknown antecedents, 
— analysis of the complex facts presented to our obser- 
vation. The whole difference between sound and un- 
sound generalisation lies in the care with which we seek 
for hidden elements in the cases observed, which shall 
modify our first rough guess at the law supposed to 
explain them. 

Accordingly the attack on a generalisation most 
usefully takes the shape of an attempt either directly to 
point out hidden circumstances in the facts observed, 



280 FALLACIES. [Pabt IL 

or at the least to point out that the analysis has not 
been a remarkably searching one. Thus Prof. Tyndall, 
attacking the theory that Bacteria are capable of ' spon- 
taneous generation/ sums up the chief faults of the 
argument as follows : — 

" The proof of Bacterial death at 140° Fahr. consists solely in the 
observed fact, that when a certain liquid is heated to that temperature 
no life appears in it afterwards ; while in another liquid life appears 
two days after it has been heated to 212°. Instead of concluding that 
in the one liquid life is destroyed and in the other not, it is assumed 
that 140° Fahr. is the death- temperature for both ; and this being so, 
the life observed in the second liquid is regarded as a case of spon- 
taneous generation. A great deal of Dr. Bastian's most cogent reason- 
ing rests upon this foundation. Assumptions of this kind guide him 
in his most serious experiments. He finds, for example, that a 
mineral solution does not develop Bacteria when exposed to the air ; 
and he concludes from this that an organic infusion also may be thus 
exposed without danger of infection. He exposes turnip-juice accord- 
ingly, obtains a crop of Bacteria, which, in the light of his assumption, 
are spontaneously generated. Such are the warp and woof of some of 
the weightiest arguments on this question which have been addressed 
by him to the Royal Society." 

Finding M (a component of S) followed or accompanied 
by Z, whether in numerous instances, or in one instance 
where apparently no third circumstance has had time 
or opportunity to intervene, the natural impulse is to 
state the law as M — > Z. And, in every case, attack 
on the truth of such law consists ultimately either in 
the direct assertion that certain instances do in fact 
contradict it, or in the milder assertion that no steps 
have been taken to limit the sweep of the law as far as 
prudence would suggest; or in the still milder shape 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 281 

of an inquiry whether or no such steps have been taken. 
If, in the case observed, M or Z was really qualified by 
the presence of N, it is always possible that the real 
law may be N — > Z, or MN — > Z, or M — > ZN, or 
MN — > ZN ; that is, N may be an important factor, 
and any statement of the law which neglects to mention 
it may accordingly be inexact and misleading. 

In the Appendix it is noticed that the five methods 
consist really of variations upon two that are funda- 
mental. These two are the Methods of Agreement 
and of Difference. It is questionable, however, whether 
the distinction even between these two is of real import- 
ance from our point of view. As regards observed 
coexistences, the Method of Difference is plainly alto- 
gether inapplicable until they are resolved into sequences 
(which is often at present practically impossible) ; but 
as regards sequences the distinction depends merely on 
the fact that in employing the Method of Agreement 
•' unknown circumstances ' are eliminated chiefly by the 
number and variety of observations, while in employ- 
ing the Method of Difference it is chiefly the immediacy 
of the sequence (known through our control of surround- 
ing conditions) that is relied upon for the same pur- 
pose. But in both we may be deluded, and by the 
same cause. The case or cases upon which we rest our 
theory may really belong to a narrower class than that 
which the theory contemplates. Their differentia over 
the genus about which we make the assertion, may be an 
important factor in the behaviour of the things observed. 



282 FALLACIES. [Part IL 

The Five Inductive Methods, with all their unlike- 
ness to each other, have thus one important point of 
similarity. They all consist in bringing cases, — claimed 
to be unmistakable on account either of their ' nature ' 
and circumstances, or their number and variety, — cases 
of the operation of the law set up as Thesis, and of no 
more complex one. And consequently the one point of 
vulnerability for all of them is the possibility that the 
cases relied upon were somehow different from those 
expressly covered by the law ; that, in fact, there were 
special circumstances along with them, which should be 
generalised so as to find expression in the statement of 
the law, making it narrower than at present. 

The five methods are not in themselves a set of 
separate safeguards against inductive fallacy, or a com- 
plete exposition of the modes in which we ought to 
reason from fact to law ; but rather a generalised analysis 
of some of the most elementary modes in which we do 
(or perhaps, did originally) so reason ; each of these 
modes being liable to its own special dangers, and there- 
fore, unless properly guarded, each and all being illusory 
as a guarantee. Regarded simply as methods of Proof, 
they are in several ways not quite satisfactory. They 
are in this dilemma : either they are to be used as actual 
tests, to which we can bring the given experiment, — in 
which case they are certainly liable to ' frustration ; ' or 
else they are merely ideals to which in practice we can 
never be sure that we attain. Moreover, they assume a 
greater simplicity of material than really ever exists, and 



Chat. VI.] THE EMPLOYMENT OF GUESSWOEK. 283 

they assume too that the mind comes to its work of 
interpreting the facts of experience in a state of candour 
and virgin ignorance which is— ever since language took 
shape — very far from being the actual case. Their 
practical value, therefore, is rather as systematic hints 
for tentative discovery, than as methods of Proof at all. 

How then is our general knowledge proved from the 
particular facts of experience ? It can be disproved by 
experience easily (subject of course to the familiar 
possibility of our supposed experience being itself illusory), 
but proof of an abstract proposition can never be theoreti- 
cally complete, and the lines which we draw across the 
long scale between the highest practical certainty and 
the wildest guess-work are, like all our distinctions in 
continuous nature, useful up to a certain point but 
incapable of standing close scrutiny or careful refine- 
ment. The truth that destruction is easy and construc- 
tion difficult, is nowhere better exemplified than in our 
proof of general laws. A sequence in Nature is observed 
to happen frequently ; this perhaps sets some ingenious 
inquirer on the track of a law ; experiments (we are 
speaking, of course, of modern times), are made with the 
view of testing the hypothesis, — of narrowing down the 
law into definiteness and limiting it as far as necessary. 
At last, after many struggles it comes forth as a recog- 
nised empirical law. But now it either remains in this 
condition, with the sword of possible contradictory 
instances ever hanging over its head, or by some further 
discovery it gets established under the protection of 



284 FALLACIES. [Part II. 

some wider law with a greater prescriptive right. Now, 
if it be false, this wider law must be false also. Perhaps 
it is secure at last ? Perhaps it may be ; practically it 
often is, but theoretically never. For every supposed 
law has merely served its purpose and stood its tests 
(such tests as we can apply) for a certain finite length 
of time. After centuries of life it may be upset in a 
moment, or at least found to be not universally true, to 
be true only under conditions, to be crude in its present 
statement and to need further refining away. The 
longer it has stood its trial, the safer of course it is 
against the fear of contradictory instances coming to 
light; in fact, it has probably been pared down already 
to accommodate such instances a dozen times, being of 
course narrowed each time. 

It is an ungrateful task for any one who cares about 
the distinction between truth and error, to dwell on such 
facts as these, without some further apology. They 
seem at first sight to prove too much, — namely that 
there is no certainty ever attainable in interpreting 
Nature, but that ' unknown antecedents ' are as 
ubiquitous, and possibly as destructive to our best theories, 
as the dangers to health in the midst of which our lives 
are passed. Nor do I, in fact, see any way of denying 
this except by means of deliberate self-deception. But 
such apology as I can make for this view will come 
better in speaking, at the end, of some of the defences 
that can be made for Logic as a practical science. 

Of course, in the case of a great many laws believed 



Chai\ 71.] THE EMPLOYMENT OF GUESSWORK. 285 

in, the question is settled for us by ancestral habits ; and 
in many other cases we shall accomplish more in the 
world by faith than by scepticism. But here we are 
merely trying, for the moment, to see the facts as they 
are, and not as practical prudence might suggest that we 
had better habitually view them. And two things, I 
think, we cannot help admitting : — 

First, that every supposed law, whether of succession 
or coexistence, may turn out to be too widely stated. 
If, as is probable, there is ' some truth in ' such law, yet 
the assertion it makes may be too wide and sweeping, 
and perhaps ought to be limited in some way, making 
it true only under certain conditions. 

Secondly, between mere guesses, hypotheses, theories, 
empirical laws, and 'laws of Nature/ there are only 
continuous differences of degree in certainty, according 
to the nature and number of the tests they have stood, 
and the duration of their past invulnerability. In the 
case of Axioms, so far as their contradictory is incon- 
ceivable — i.e. makes nonsense of the words employed, — 
so far of course it is futile to speak of their uncertainty ; 
but wherever this is not the case, Axioms too come 
merely at the head of this same scale of credibility. The 
resemblance in uncertainty between a fanciful guess and 
a proved law may be less important than the difference 
in degree of certainty: but the fact cannot be safely 
hidden that the resemblance exists. 

The distinction often made between valid inductions 
and 'merely empirical laws' is then, strictly speaking, 



236 FALLACIES. [Part II. 

not absolute, though roughly useful; the line between 
them will not bear close inspection. For 'empirical' 
means ' true so far as we can yet see, but, inasmuch as 
inexplicable at present by a higher law, possibly liable to 
further limitation ; ' and this may be said of every Law 
of Nature we possess. The method of proving laws is 
one and the same whether they be the merest wildest 
supposition or the soundest explanation of the facts of 
Nature. In the first place it is a sine qua non that no 
contradictory instance shall have yet been found. It 
hardly needs expressly stating that one single discovered 
exception is sufficient to break down an asserted law. 
The absence of such an instance, however, it must be 
equally obvious, is not sufficient for proof. But, in the 
second place, the positive strength of our evidence de- 
pends upon the extent of our right to claim sufficient 
knowledge of all the attendant circumstances of the 
observation or experiment. 

IV. The Dangers of the Argument by Sign. 

Under Deductive Proof, it will be remembered, we 
have elected to leave aside the case of complete Demon- 
stration, since to supply a missing premiss correctly is 
at least as difficult as to pass it for sufficient when 
already expressed. It is not, however, with the whole 
problem of supplying missing premisses that we are 
now concerned : that belongs by right to the method for 
reducing to absurdity. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 287 

What is here called the argument by sign, as opposed 
to the argument by example, consists of the cases where 
the major premiss is either itself given as Reason, or is 
only suppressed through its extreme familiarity, not 
through any doubt as to its truth or any hesitation as to 
what the law may really be. When, e.g., we attempt to 
prove innocence by means of an alibi, we refer no doubt 
to the principle (which hardly needs express statement) 
that a man cannot be in two places at once ; and so, in a 
large number of instances, where the application alone is 
expressly given, the argument is really intended for deduc- 
tive. In all cases of attempted proof, it is experience in 
some shape or other that is relied upon, whether already 
generalised experience or not ; experience crystallised 
into names and propositions, or experience not yet so 
formulated. The difference between empirical and de- 
ductive proof may be further brought out by saying that 
in the former we deal more directly with the facts expe- 
rienced, while in the latter we rely largely on mere for- 
mulas. 

The chief difficulties in summing up the dangers 
peculiar to the Argument by Sign lie partly in the fact 
that faulty deduction may be due to so many different 
causes, and that, through disclaiming one cause while 
allowing another to operate, the fallacy has so many 
facilities for escaping open conviction ; and partly in the 
fact that according to our own definition, it is only when 
both Principle and Application are clearly apprehended 
as such, that any argument can be rightly called deduc- 



288 FALLACIES. [Part II. 

tive, and that consequently if an attempt is made to 
employ a Principle that does not strictly apply, it may 
easily be pleaded against the charge of faulty deduction, 
that strict deduction (Demonstration) is not intended. 

Nevertheless something may, I think, be done, by 
recognising clearly that the danger against which every 
argument professedly deductive has to guard is the ac- 
ceptance of a Principle which does not apply ; and this, 
whether caused through ignorance of syllogistic require- 
ments, or through verbal ambiguities, or through suppos- 
ing the reciprocal of either Principle or Application to be 
its equivalent. Against the easy plea that demonstration 
is not intended, may be brought the reminder that in such 
case the Thesis, so far as definitely asserted, is at first a 
pretender to qualities which it afterwards confesses to 
be wanting. So far as it really cannot be rationalised, — 
by bringing the underlying principle and its application 
into shape for rigid investigation, — so far its truth must 
of course remain untested, and belief in its truth either 
a careless or a semi- voluntary act. 

It may be well, then, to glance at the operation of 
the three causes of faulty deduction just above enume- 
rated. And first, of the ignorance of syllogistic require- 
ments. By this is meant solely the ignorance, when 
Reason and Thesis are given, of the fact that a further 
assertion is implied, and of the nature and limits of such 
further assertion, — what must be said by it, in order to 
complete the deductive proof. 

It may be held, and it may be true, that in actual 



Chap. VI.] THE EMPLOYMENT OF GUESSWOKK. 289 

practice purely syllogistic fallacies very rarely occur. 
What on the face of them appear like syllogistic fallacies 
may in most cases be found on further inquiry to be 
really due either to false belief as to the matter, or to the 
tyranny of names, or to ignorance of the law of Counter- 
Indication, whereby the reciprocal of some true Principle 
is accepted as equivalent in meaning. Thus if any one 
argues that the prisoner is guilty, from the fact of his 
confusion when arrested, it is, no doubt, more probable 
that he believes in the truth of the further assertion 
' confusion — > guilt/ or in the equivalence of this with 
the less questionable law that ' guilt causes (and there- 
fore — >) confusion,' than in the formal sufficiency of the 
latter assertion as completing the Syllogism. Still, easy 
and indeed self-evident as the formal requirements of 
reasoning are, we are bound to suppose that people are 
occasionally liable to look upon insufficient premisses 
as formally binding. In fact, there is probably one class 
of persons who have really acquired some power of con- 
fusing themselves in this matter, namely, those who, 
having learnt the moods and figures by rote for an 
examination, have not as yet quite succeeded in forget- 
ting them again. Nothing could well be more confusing 
than an attempt to apply the cumbrous machinery of 
the Syllogism to arguments met with in real life. And 
whoever has tampered with his mother-wit by substi- 
tuting for it a clumsy Logic depending on elaborate 
mnemonics, must no doubt pay the penalty in loss of 
power, so long as the mischief remains. 



290 FALLACIES. [Part II. 

It is well, therefore, to remember that the Syllogistic 
requirements may always be clearly shown either by 
viewing the middle term as a sign, the universal trust- 
worthiness of which sign is all-important to the proof; 
or, where the middle term is difficult to find, by viewing 
R as itself the affirmation of the antecedent (or the denial 
of the consequent) of a hypothetical proposition of which 
T (or the denial of T) forms the other term. It is not 
necessary in this place, however, to enter fully into the 
details of this operation, since in the chapter on Reduc- 
tion to Absurdity (p. 298) we shall find a better opportu- 
nity for doing so. In the mean time, apart from igno- 
rance of syllogistic requirements, and from the possibility 
that our supposed knowledge relied upon may be mis- 
taken, there remain two other, and commoner, sources of 
error. 

As regards the acceptance of the reciprocal as equiva- 
lent, not much more remains to be added to that already 
said. Either the Principle or the Application may be 
wrongly supplied in this manner, with the result that 
we then accept an express principle, together with an 
express supposed application thereof, when in fact the 
latter is merely the application of a very different prin- 
ciple, — and one, it may be, very much easier to prove. 
Especially is this the case, as pointed out above, in the 
disjunctive (or dilemmatic) argument : M — > non-££> is 
nearly always easier to establish than non-M — > £& ; 
and accordingly, wherever in a deductive argument the 
R states that S — > non-M, we need to be especially on 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 291 

guard. But in all cases of attempted deductive proof, 
this fallacy is a constant source of danger. And its in- 
sidious nature and the facilities for escape which, even 
when detected and arrested, it presents, mark it out as 
deserving very careful attention. 

So great are the facilities for escape that it is difficult 
to find instances which will be unhesitatingly accepted as 
such, even by a respectable minority of readers. The 
danger is so simple, so obvious when pointed out, that 
those who nave not had occasion to study the causes 
of fallacy in actual operation will be loth to accuse the 
human intellect in general of ever being in the least 
affected by it : while even those who have watched the 
action of erroneous reasoning most carefully must hesitate 
to say in the given case that this cause was solely, or even 
mainly, operative. The logician is in fact here placed in 
much the same difficulty as so frequently occurs in all 
interpretation of motives: several motives have had a 
share in some action, and amongst them, in the vaguest 
and most unconscious manner, one motive less noble than 
the rest ; a motive which the person accused will be not 
only sure to deny, but which, if he had been conscious of 
it at the time of acting, he would at once have dismissed 
as unworthy. As a matter of fact it may have had con- 
siderable weight, and yet if the case is brought forward 
as an instance of its operation, a feeling of perfectly 
honest virtuous indignation is aroused. So it is w T ith 
this deductive fallacy. A person who has really been 
partly misled by it will be almost sure to declare, when 



292 FALLACIES. [Pabt II. 

the fallacy is pointed out, either that he meant the 
Principle to cut both ways, or else that he only intended 
to make a suggestion or to raise a presumption, — " com- 
plete demonstration being unattainable : " and quite 
probably both of these intentions were really present 
to his mind in a vague way, along with some uncertainty 
as to what the requirements of complete demonstration 
might be. For just as a man is seldom conscious of his 
own motives at the time, while on after reflection the 
nobler motives are apt to rise into undue prominence, 
so our view of what constitutes complete demonstration 
is often clearer on after reflection than in the heat of 
argument or during the first glow of belief. 

Nevertheless, there is on occasion something gained 
by forcing even the most unworthy motives into promi- 
nence, in order that they may be definitely disclaimed 
and the disclaimer registered for future use ; and so with 
this kind of fallacy. Where the argument is plainly 
intended for deductive, time may often be saved by 
searching first for any slackness in the view of what de- 
ductive proof really demands. If on inquiry it turns out 
that the intention was merely to raise a loose presumption 
in favour of the view, the looseness of the presumption 
may be thus made fully evident : while if the reciprocal 
of the express principle is believed to be also true, this 
belief can then be placed on its trial. 

The remaining source of danger in deductive argu- ' 
ments may be described as that of forgetting part of the 
postulated meaning of the names employed, or again, of 



Cjiap. VI.] THE EMPLOYMENT OF GUESSWORK. 293 

reading into them meanings which they are not intended 
to bear. So far as significant names are employed in 
Proof (whether as M or S or §b) the two liabilities to 
arror are at bottom the same as those already men- 
tioned, — undue neglect of difference or of resemblance. 
The meaning of every name, we have seen (p. 108) 
contains two elements, — the differential and the generic, 
— and either of these may be unduly overlooked. We 
may, in other words, unduly neglect the negative or 
the positive meaning, the points of difference from other 
things or the points of resemblance to some of them, 
to which the name refers. 

This double chance of error is one that was treated 
at some length by Aristotle, under the name of the 
Fallacia Accidentis, or confusion of the accidental with 
the essential. It is true that if we interpret Fallacia 
Accidentis as widely as possible, it will include far more 
than these merely verbal errors, namely, the errors also 
to which empirical proof, as such, is liable. When we 
reason by false Analogy, or when we explicitly frame too 
sweeping a generalisation, we are taking 'accidental' 
resemblance for essential (or essential difference for acci- 
dental) ; and vice versa when we fall short of the ideal 
on the other side ; but it was the interpretation of names 
that Aristotle seems to have had chiefly in view. There 
is another phrase also sometimes applied to the same 
double chance of error ; the possibility of arguing a dicto 
simpliciter ad dictum secundum quid, or a dicto secun- 
dum quid ad dictum simpliciter; and perhaps this 

supplies the more really descriptive title. 
14 



294) FALLACIES. [Part II. 

Everything that can be named may be viewed as 
existing at once simpliciter and secundum quid (or as 
belonging to a genus and also possessing a difference). 
Everything belongs to certain classes, the narrower * of 
which possess difference over and above the broader, and 
beyond the narrowest of all remains any real individual 
peculiarity of the thing in question. Accordingly any 
general name we give to a thing neglects of necessity 
more or less of its secundum quid, and yet in order to 
employ deductive proof we are obliged to use general 
(i.e. significant, or indicating) names. S may be rightly 
called M, but it is also always something more : all 
depends (as we have seen in speaking of Analogy) on 
whether the something more is important or unimportant 
(essential or accidental) for the purpose in hand. 

But suppose that the difference is ruled unimportant 
and that M is decided to fairly deserve the name of §^, 
that name in turn has a differential and a generic meaning, 
either of which may be unduly overlooked ; and so on for 
ever. Take the name '■ man.' Because a man is certainly 
an animal, or a ' creature/ or even a ' thing,' or a ' figure/ 
or an 'object,' we do not thereby gain the right to forget 
the differential qualities due to his human nature: nor 
on the other hand does the fact of his rationality do 
away with the chain that binds him to the wider class 
of ' animals,' or with the consequences (such as mortality) 
therein implied. If men, through developing their differ- 

* I.e. narrower by direct limitation, not merely those which happen to 
have the fewest members. 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 295 

entia from beasts still further, should eventually manage 
to conquer death, some of our old nomenclature would 
require remodelling, but the logical law would of course 
remain unaltered. 

The traditional examples of this fallacy are valuable 
rather as being unmistakable than as really representative 
of the difficulty involved. " You are not a man j for a 
man is what I am, and you are not what I am," or " You 
ate raw meat to-day ; for you bought raw meat in the mar- 
ket yesterday, and to-day you ate that which you bought 
yesterday in the market." Practically such catches as 
these are obvious to any child, and in order to exemplify 
the working of the real danger we must choose a finer 
shade of it. For this purpose the best examples of 
neglecting difference are perhaps the cases where some 
judgment is based upon what may be called a partial or 
one-sided view of the S : where the name with which 
the S is labelled is incompletely defined, defined by genus, 
without the full differentia ; as where a soldier is said to 
be " a man who makes a contract with his country to kill 
anybody whom his country wishes to have killed." In 
reality, of course, the soldier does not make this contract 
simpliciter, but there are other elements in it, which 
when taken into account may perhaps alter radically our 
opinion of his merits. Or again, voluntary death is some- 
times heroic ; and suicide is certainly always voluntary 
death, — but with a difference added. Voluntary death is 
the genus under which ' suicide ' comes, but the specific 
difference is just the fact that the motive is merely 



296 FALLACIES. [Pabt IT. 

to escape, for ourselves, something which, rightly or 
wrongly, we regard as worse than death, not a • heroic ' 
thoughtlessness for ourselves and regard for the good of 
others. 

For examples of neglecting resemblance we may take 
the cases where difference is believed to be thorough- 
going or fundamental, merely, or mainly, from the fact 
of different names being used. Readers of Newman's 
Grammar of Assent will remember, for instance, the 
importance there given to the difference between an 
assertion and a conclusion. The two names are different, 
and the two things are certainly so far different that an 
assertion may sometimes be made "without grounds," 
while a conclusion (by its definition) presupposes grounds, 
weak or strong. But a conclusion means, of course, an 
assertion and something more : it belongs to the genus 
assertion, but possesses also the differentia " reasoned." 
Newman indeed prefers to say (p. 2) that an assertion has 
"got beyond being a mere conclusion," but by this it 
appears (p. 4) he means merely that unhesitating faith 
is stronger than faith which (p. 1) consciously depends on 
a prior condition being true. His interest, however, is 
to make out that a conclusion is radically different from 
(i.e. does not even belong to the genus) assertion, and for 
this purpose he dwells at some length on the specific 
difference (the presence, and the absence, of reference to 
grounds).* 

* It should be mentioned, however, that at the end of the section 
(p. 6) this is felt to be hardly sufficient, and another supposed point of 



Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 297 

difference has to be brought forward, resting on a less interesting or 
important verbal confusion. " We cannot give our assent to the proposi- 
that * x is y ' till we are told something about one or other of the terms " 
[I should rather say, both the terms] ; " but we can infer, if ' x is y, and y 
is z, that x is z,' whether we know the meaning of x and z or no." The 
merest beginner in logic will recognise at once that ' x is z ' does not 
stand here for a single, meaningless, proposition, but merely for an 
indefinite variety of possible propositions with a meaning. All that is 
said in saying that in such a case we recognise the reasoned truth 
of 'x is z' is that (with these premisses admitted) we see clearly that 
x, y, and z may mean anything whatever, without affecting the validity 
of the conclusion. 



CHAPTER VII 

KEDUCTIO AD ABSUEDUM. 

Having thus spent some trouble over the inquiry what 
can be done to improve our methods of finding offhand 
the source or cause of a piece of faulty reasoning, it is 
with a feeling of relief that we now turn away from the 
difficulties of guesswork, treading again upon firmer 
ground. Any discussion of the best means of promptly 
discovering the actual seat of a fallacy is likely to raise 
more difficulties to the mind of the thoughtful reader 
than it can settle for him. He will feel, at the end, that 
educated tact and insight are of higher value for such a 
purpose than any number of condensed rules can be. 
The special circumstances encountered in actual argu- 
ments are plainly too various to admit of hard and fast 
legislation, and the most that can be hoped is that some 
aid may have been given in clearing away preliminary 
confusion; rendering it to that extent more easy for 
further small advances to be made. But now there 
remains the question, Where guesswork fails, what then ? 
The answer has been briefly given already, — once, and 



Chap. VII.] REDUCTIO AD ABSURDUM. 299 

directly, on p. 174, and on other occasions (as on pp. 27, 
114, 213) by implication: but it now becomes necessary 
to deal more fully with it, and to show what is meant 
by "applying the method with sufficient fairness and 
caution." 

The Reduction to Absurdity, it was also said above, is 
a method of raising objections which is ultimately appli- 
cable in all cases without exception; and the plans of 
attack already hinted at are only to be preferred to it on 
the ground of their greater directness in certain cases. 
It should, however, be at once explained that the name 
* Reduction to absurdity ' is here to be employed in a 
somewhat narrower sense than usual. To reduce any 
assertion,— simple assertion or argument, — to absurdity 
is always, at bottom, to bring it somehow into conflict 
with observed or admitted fact ; and this may of course 
be done in various ways. For example, to produce a 
contradictory instance might fairly be called a mode of 
reduction to absurdity : or again, more widely still, to 
bring to light the absurd consequences of any hypothesis. 
But, as applied to arguments, rather than to assertions 
in general, we may define the process of reducing to 
absurdity more narrowly, restricting it to one special 
method, in default of a better name to use for the purpose. 
In all arguments as a last resource — and in some even 
as the most direct attack — we have the power of com- 
bining R and T, inquiring what they together imply, and 
then comparing such further assertion with observed or 
admitted facta For simplicity let us denote " required 



300 FALLACIES. [Part II. 

further assertion" in every case by the letter F; then 
the reduction of an argument to absurdity (as the name 
will here be used) means the objection that, T and R 
being given, F is untrue* 

The fact that every Thesis deductively proved, — every 
syllogistic conclusion — rests upon some law, or Prin- 
ciple, from which its deduction takes place, has been 
already sufficiently noticed, the two premisses of every 
Syllogism being respectively : — 

(1.) The major premiss, — the statement of such law : 
and 

(2.) The minor premiss, — the application of it to the 
case in hand : 
and whichever of these be given as R, the other is implied 
before R's 'formal adequacy' is complete. But now it 
remains to be said that every R must be translatable into 
one of these, — major or minor premiss, — before we can 
proceed to fully test the argument. f This was in fact 
the meaning of saying that all Proof, so far as really 
Proof, is deductive, and that the Syllogism is " perfectly 

* It must be noticed that F is not contained in the meaning of T 
and R together in the same way exactly as T is contained in the mean- 
ing of R and F; but it is as truly implied by them nevertheless. And 
if that which T and R together imply be found untrue, the argument is 
clearly overthrown : for R, regarded as a firm support for T, is found to 
require as true a proposition which is in fact (or by admission) 
not bo. It makes no difference whether F be Principle or Applica- 
tion : unless both of these are true, T remains without the required 
foundation. 

t Hence a prior condition to the employment of the method is agree- 
ment as to the meaning of the assertions made in T and R. 



Chap. VIL] EEDUCTIO AD ABSUKDUM. 301 

general in its operation : applies to all Proof whatever, 
and is not an engine to be used in deductive inference 
merely." That is to say, whenever any Reason is given 
for any Thesis, a knowledge of syllogistic requirements 
will enable us to see how far such attempted Proof falls 
short of Demonstration ; or, in other words, to see what 
further assertion must in every case be added to R before 
its formal adequacy is complete ; — before all has been done 
except to inquire whether R is true in fact. Wherever 
any Reason is given for any Thesis, and the special 
dangers of the argument are not immediately apparent, 
hostile criticism falls back at once on the inquiry, What 
are the gaps in the reasoning that possibly require to be 
filled? 

The Axiom of the Syllogism, whether stated in ■ ex- 
tension ' (i.e. with direct reference to the ' things ' spoken 
of), in the famous Dictum de omni et nullo, — which 
being rendered into English says in effect," " Whatever is 
asserted (affirmed or denied) of a class is asserted of any 
part of that class," — or in comprehension (i.e. with direct 
reference to the judgment made) in the equally famous 
Nota notce, which we may translate, — " A sign (S) of a 
sign (M) of §?, itself indicates gj " j — the Axiom of the 
Syllogism requires, for purposes of Proof, to be postu- 
lated true in its 'reciprocal' form. The statement so 
obtained might be not improperly named the Dictum 
de singulo or the Kota rei ipsius. It says that in 
order 10 prove anything true of a single thing (whether 
object, quality, event, or whatever the thing may be) 



302 FALLACIES. [Part II. 

it must also be shown to be true of a whole class of such 
things, a class including the one observed. Or, stated in 
comprehension, — In order to prove that S — > *£», S 
must be shown to indicate M, a sign of §fe. 

Let no one think these postulates either a valuable 
discovery in Logic, or an unwarranted and presumptuous 
innovation. They are merely another way of making 
the familiar assumption that "Nature is uniform," or 
that there are 'laws' of sequence and coexistence. It 
is on this assumption that all explanation, classification, 
and prediction necessarily proceed. Without it the 
Universe would be a chaos of exceptional cases, — it 
'exceptions' can be pictured apart from 'rules' at all. 
Every individual thing represents a class, of which it is 
a member; everything belongs to some genus, besides 
possessing a differentia. Accordingly, whenever any fact 
is appealed to as reason for believing any assertion, the 
important matter is to get the supposed underlying law 
(or laws) clearly stated; and the central difficulty in- 
volved is that of really rising above the individual case 
while at the same time avoiding the unfairness, or the 
pedantry, of insisting that a wider, and therefore more 
vulnerable, law is implied than the assertor really in- 
tends. It is true that R is sometimes, though seldom, 
the statement of the law itself, — as in the argument that 
" Protective duties are economical : for whatever brings 
in money enriches : " or again, " The farmers will not pay 
in rent more than the net produce of their farms, for no 
trading class will continue a losing business." But here 



Chap. YII.J REDUCTIO AD ABSURDUM. 303 

no real difficulty can arise, except through verbal 
ambiguities, and, sometimes, through uncertainty as to 
the Law of Counter-indication The finding of the 
Application when the Principle is clearly expressed must, 
from the nature of the case, be always an easy matter. 
Supposing that, in the first of the two instances just 
given, — their truth or cogency does not interest us here, 
— " enriches " and " are economical " are used in the same 
sense, it needs no Logic to tell us, at this stage of the 
work at least, that the formal adequacy of the Reason 
depends on the further assertion that " Protective duties 
bring in money." If a Principle is laid down as Reason, 
even a child can seldom fail to see that its force as 
Reason depends on its being connected, in the only way 
possible, with the Subject of the Thesis. Of course there 
are cases conceivable, where, through accepting the reci- 
procal as equivalent, a wrong application may be made. 
But this danger has been already sufficiently discussed. 
We need not here go back to the pons asinorum of 
Logic. 

We have to deal, then, solely with the case where R, 
if relevant at all, is not itself the Principle, but is either 
(1) directly, or (2) remotely, the Application. By a 
1 remote ' Application is meant the case (briefly referred 
to on p. 210) where the S of the thesis is not expressly 
mentioned by the Reason. But first of the case where 
the Application given is as direct as possible. That is, 
where something is distinctly said about S as a reason 
for believing the assertion made of it ; as in ' Gold can- 



304? FALLACIES. [Part II. 

not be produced artificially, for it is an elementary sub- 
stance/ or ' Whales are not fishes, for they breathe by 
lungs/ or ' He must be in London, for he is not at his 
country house/ 

The whole difficulty here is as to the extent of the 
Principle really involved. Is it, for example, ' To be an 
element — > incapability of artificial production/ 'To 
breathe by lungs — > not to be a fish ' (the counter 
equivalent of 'To be a fish — > not to breathe by 
lungs '), ' Not to be at one's country house — > to be in 
London' (i.e. 'All who are not at their country houses 
are in London ') ; or is it the narrower assertions, ' Gold, 
if an elementary substance — > incapability of, etc./ 
' Breathing by lungs, when found along with the other 
attributes of a whale — > non-fish/ ' If he is not at his 
country house, he must be in London ' ? The answer to 
this question furnishes the key to the distinction between 
fair and unfair employment of the method for reducing 
to absurdity. The difference between what Logic might 
be, and what it too often is (what perhaps its less thought- 
ful enemies suppose it always to be), is much like the 
difference between fair and unfair caricature : a difference 
not so much in the thing itself as in the manner in 
which it is interpreted, and the occasions on which it is 
employed. It is chiefly the inability to keep this dis- 
tinction clear which has made it possible for orators to 
describe the Syllogism as "a contrivance for catching 
you in a trap and holding you fast in it." 

Just as the middle term in a Syllogism (the term 



Chap. VII.] EEDUCTIO AD ABSURDUM. 305 

appearing in both premisses) may always be viewed as a 
sign, or mark, possessed by S, — a mark which, abstractly 
indicating (or being a universal sign of) §5, is employed 
to prove the conclusion; so, conversely, that which is 
asserted by R as indicated (abstractly or concretely) by 
S, may always be viewed as the middle term of a Syllo- 
gism which has yet to be completed. If S is only known 
to be §3 because it is M, M is (according to the Dictum 
de singulo) thereby asserted to be universally a sign 
of §3. If S is only known to be §5 because, being iV, 
it is M, M, when specially limited in this manner by 
N, is thereby asserted to be universally a sign of §5.* 
The proposition MN — > §j» is of course just as truly 
1 universal ' as M — > §5, though of narrower sweep. 

Are we then, whenever we meet, put forward as 
Reason for any Thesis, a minor premiss which is bare of 
special limitation, to assume that no special limitation 
was present to the mind of the person so putting it for- 
ward ? Yes, and No. For the purpose of getting the 
principle expressly defined, it is often highly desirable to 
assume, provisionally and fictitiously, that the wide Prin- 
ciple, as strictly implied by the reasoning, was believed 
to be true. By this means wavering uncertainty as to 
its falsehood may often be destroyed, and even where no 
shade of such hesitation existed it is a clear gain to get 
the real principle reduced to definiteness. But if we go 
beyond this employment of the method, we ourselves 

* E.g. ' S is guilty (S) ; since, (N) though the charge is one that an 
innocent person would readily contradict, it has (M) never yet been 
expressly contradicted.' 



306 FALLACIES. [Part II. 

commit probably the greater error of the two. Thus 
while no objection would perhaps be raised to demanding, 
as Principle for 'Gold cannot be produced artificially, 
since it is an element/ the assertion that 'all elements 
are incapable of artificial production/ it is obviously un- 
fair to demand as the Principle strictly involved by ' He 
must be in London, since he is not at his country house/ 
the assertion that 'All who are not at their country 
houses' — still less 'All who are not at his country 
house ' — ' are in London/ thus neglecting the fact that 
other alternative places of residence exist. The absur- 
dity, if we made such a demand, would rather lie with 
ourselves. In such a case as this, since there could not 
be any hesitation as to the suggested Principle being un- 
true, we should probably dispense with even the ficti- 
tious and provisional assumption of it, cutting the process 
short by asking at once what the special circumstances 
are which are supposed to limit him (not ' all men ') to 
one place or the other. But there are plenty of really 
doubtful cases. Take further the argument 'He must 
be ill : for he has lost his appetite/ Here the principle 
really believed as foundation might be that 'loss of 
appetite universally indicates illness ; ' or, on the other 
hand, it might be merely ' if he has lost his appetite he 
must indeed be ill/ — the special circumstance thereby 
indirectly hinted being of course that S's appetite is 
known to be of a particularly unfailing kind. If the 
latter were the true explanation, we should of course 
make a grave mistake in attempting to lay upon the 



Chap. VII.] REDUCTIO AD ABSURDUM. 307 

assertor the burden of supporting the truth of the wider 
assertion; but we should be quite right in giving him 
the choice between doing so and narrowing it down into 
a shape that will fit the facts. 

The method of reducing to absurdity should, then, be 
regarded rather as a method of putting questions than of 
making a direct assertion that an absurdity is necessarily 
implied. We can never really get so far behind the 
scenes of another person's mind as to attain complete 
security in guessing what the exact Principle relied upon 
has been. We can only say that the Principle which 
appears to us to be implied by the express statement is 
so and so, and that we presume he hardly intends, in 
fact, to rely on any such plain absurdity. He must 
either narrow it for our benefit, or be content to leave us 
unconvinced : we certainly cannot accept the argument 
as it stands. So far as the Principle fails to attain some 
generality wider than the T itself, so far the T remains 
unrationalised, — i.e. without a logical foundation : so far 
as the principle sacrifices security for the sake of gene- 
ralisation, so far the foundation is unsound. We do not 
catch the assertor in a trap : we merely show him that 
he has chosen to place himself in a dilemma : and we 
then request him, for our enlightenment, to choose which- 
ever alternative he himself prefers. If for any reason he 
does not like to rationalise his thesis by committing him- 
self to any definite Principle, it is always open to him to 
be content to leave us unconvinced. 

But there is a sense in which this may be called 



308 FALLACIES. [Part II. 

stating the alternatives a little too baldly. In a certain 
sense there may be a flaw in our conviction, and yet not 
a serious chasm. There is a middle ground between 
complete Demonstration and total failure to justify belief. 
There are, in a sense, different shades of certainty; 
evidence varies in strength. Where we cannot get an 
assertion completely demonstrated from a definite and 
faultless principle, the next best thing is to demand that 
the Principle shall, if vague, be as unexceptionable as 
possible ; if sound, as simple as possible ; and that we 
shall know, even incompletely, what the Principle really 
is, and to what extent it may be trusted. Knowledge, 
even when in the empirical stage, is often better for 
practical purposes than pure ignorance would be. And 
this leads us to speak of the sole remaining case, — where 
the Reason is ' remotely ' the Application. 

When, for example, I argue by Analogy, and equally 
when I base a law on facts observed, nothing at all is 
said in the Reason about precisely the S of the Thesis. 
In the former kind of argument, as already seen, the 
Reason speaks of a supposed ' parallel case ; ' in the latter 
kind, of ■ This (or these) S ' only, not of ' All S ' as in the 
Thesis. So again in such (very common) deductive argu- 
ments as ' A storm is brewing, for the glass has fallen 
rapidly/ or ' My friend is out, for there is no light in 
his window ; ' here the respective theses speak of ' a 
storm ' and ' my friend/ while the Reasons speak of ' the 
glass/ and ' a light in the window/ In perhaps the 
majority of actual arguments we cannot say, without 



Chap. YIL] REDUCTIO AD ABSUEDUM. 309 

great circumlocution,* that the S of the Thesis is directly 
spoken of by the Reason, and in the process of translating 
into and out of the clumsy phrases required for doing 
so, there are endless opportunities for verbal error to 
creep in. 

In the analogical and the inductive arguments, it is 
probably in most cases the simplest plan to try directly 
for unsuspected and essential difference; but there can 
be no harm in pointing out the longer method of 
arriving at the further assertion involved. The com- 
pletely definite underlying Principle differs radically 
in the two cases (Analogy and Induction), being alike 
only in the one point of being often highly complicated 
and extremely difficult to state with any exactness. In 
the argument from analogy the S of the Principle 
implied is the inventory of the (often vaguely felt and 
numerous) points of essential resemblance between the 
two parallel cases : these points of resemblance are im- 
plied by the argument to indicate Z, either universally 
or at least indifferently in the two cases before us. In 
the inductive argument the full underlying Principle 
is the statement that certain precautions in observation 
or experiment are sufficient to warrant the inference. 
These, it must be confessed, are nearly always too 
numerous for concise summation. In the presence of 
the almost infinite diversity of the circumstances in 
which observation and experiment may take place, we 

* Cf. Jevons, Elementary Lessons, p. 164. — " The circumstances of 
the barometer falling are the circumstances of bad weather coming." 



310 FALLACIES. [Part II. 

have not yet got far towards generalising the sufficient 
safeguards. Mill's five methods were an attempt in this 
direction, but, as we have seen, it is only as ideals that 
they are satisfactory, and the point of practical import- 
ance is always to know how near to the ideal the given 
experiment approaches ; for which piece of ' special ' 
knowledge an enlightened review of innumerable cir- 
cumstances, and of their bearing on the case, is needed. 

But if we cannot in these cases arrive at any full 
and definite statement of the Principle, still the method 
of reducing to absurdity may be of service in another 
way. Whatever be the S of Thesis or of Reason, the 
truth of the Reason as a whole is given as indicating 
that of the Thesis, and consequently (by counter-indi- 
cation) the untruth of the Thesis as indicating that of 
the Reason. In other words, it is always asserted that 
were the Thesis untrue, the Reason would be untrue 
also : and this, if the Reason be given as true, is clearly 
absurd. In other words again, every argument asserts 
that no theory except the thesis is compatible with the 
reason. In yet other words, that all possible rival 
theories have been examined and found wanting. 

Here we touch again upon the difficulties surrounding 
the burden of Proof. This last statement may at first 
almost appear as if, after all — to quote a former passage 
(p. 149) " the sole concern of the assertor were to frustrate, 
one by one, attempts at disproof made by the other 
side." The real case is however very different. Until 
he has shown that all such attempts are worthless, he 



Chap. VII.] REDUCTIO AD ABSURDUM. 311 

may have an underlying Principle indeed, but it must 
be one whose material truth has not yet passed our 
examination. In proportion to the extent of rival theory 
still remaining undestroyed, is the weakness of the evi- 
dence brought forward. Often these rival theories may 
all be summed up in one concise expression, and may in 
this shape be discarded en bloc. Thus in the analogical 
argument we may say that there was perhaps 'some 
cause ' for §5 being Z, which cause is inoperative in the 
case of S. That is to say, if the assertor can show some 
probability to the contrary, he has done more to support 
his assertion than if such alternative has never occurred 
to him or has been half-consciously suppressed as in- 
convenient. So in the inductive argument we may sum 
up the alternatives by saying that perhaps the law is 
stated too widely, and here again there are ways of 
showing what has been done to limit its sweep as care- 
fully as possible : and also ways of letting out the secret 
that we have gladly caught at the first explanation, and 
afterwards obstinately refused to see its obvious faults. 

In this employment, however, of the Reduction to 
Absurdity, as well as in the easier case first noticed, the 
attitude of fair investigation is still the same. The 
essential characteristic of it is that it avoids dogmatic 
assertion, and merely asks to see what has really been 
done to stop the gaps in the reasoning or to minimise 
the opportunities of error. It is noteworthy that in other 
matters also the same negative, anti-dogmatic tendency 
has always been observable in Logic. Even when Logic 



312 FALLACIES. [Part IL 

undertook to interpret to some extent the meaning of 
words and phrases off-hand, we find at least a strong 
inclination to bind them down to the least amount of 
positive assertion which the words could be supposed 
to contain. ' Some ' meant ' not-none ' instead of ' some 
only;' the universal affirmative could not by itself be 
taken to express reciprocal indication ; the Principle of 
Logical Division treats A and not-A as equal in import- 
ance; and quite recently we have had, in Mr. Venn's 
Symbolic Logic, a more consistent following out of the 
plan of interpreting statements merely by what they 
deny, than had ever before been openly and distinctly 
attempted. Logic is in far more danger of losing its 
operative power in hesitation and inactivity through 
extreme desire for fairness, than of lending any aid to 
unfair quibbling, or of trying ingeniously to make the 
worse appear the better reason. 

An additional circumstance, another straw helping 
to show the direction in which the current of Logic 
sets, may be found in the fact that so often its enemies 
are merely talkers who dislike the check that reason 
always gives to ready dogmatism; reasoners who care 
more to do their reasoning easily than correctly, or who 
have not yet become aware that any great need for 
caution exists. It is chiefly because they lack the calm- 
ness and strength required for looking difficulties in 
the face, and because Logic contents itself with asking 
whether they have really done so, that they dislike its 
methods. I do not mean, however, that the wish to 



Chap. VII.] REDUCTIO AD ABSURDUM. 313 

assert without foundation is the only explanation of all 
possible objections to Logic, and before quitting the 
subject it may be worth while even briefly to notice 
some of the more disturbing things that can be genuinely 
urged against the science. As already sufficiently ex- 
plained, however, I can here attempt to notice only those 
objections that may arise before Philosophy, — as cut 
loose from all merely practical considerations, — is brought 
to bear upon the question. 



CHAPTER VIII. 

SOME OBJECTIONS TO LOGIC. 

The practical objections to Logic, other than those merely- 
felt without the trouble of thought or inquiry, seem to 
me broadly divisible into two groups : those which claim 
that the logical attitude is on the whole useless, or 
worse ; as for instance that, consistently held, it means 
pure stagnation or scepticism, and that even a partly 
inconsistent holding of it is apt to leave us too long 
undecided : and those which admit that the end is good, 
but declare that the means are clumsy. 

The former of these is certainly the more serious 
of the two, and, as said above, I can in fact only provide 
a half-satisfactory answer. It seems impossible to deny 
that even our most careful reasoning may lead us into 
mistaken views ; and strictly speaking, the more we re- 
cognise this fact, the less room must there be for active 
faith. 

But it is one thing, after all, to admit the fact and 
quite another to admit the hasty inference sometimes 
drawn from it. It is not true that because every sup- 



Chap. VIIL] SOME OBJECTIONS TO LOGIC. 315 

posed fact is ultimately uncertain, therefore there is no 
useful distinction to be made between a careful induc- 
tion and a hasty guess. There are endless shades of 
difference here, and nothing is gained, except the 
cheapest sort of peace of mind, by shutting our eyes 
to them. If there are, strictly speaking, no degrees in 
fallibility, yet there are differences of the highest im- 
portance between the results of care and carelessness in 
reasoning. It is for the most part mere sloth, or even 
sometimes a kind of pettishness, that leads us to resolve 
to reason carelessly because with all possible care we 
may still make mistakes. Perhaps, indeed, it will be 
said that no one ever really "resolves to reason care- 
lessly," and this may be granted at once. The pro- 
cess is commonly described in finer language. It is 
• humility," not slackness of purpose, that prevents our 
asserting positively that black does not mean white. 
It is "in a spirit invincibly calm" (nor can I quarrel 
with the epithet) that we claim a vision of " loftier than 
mere material verities and wider than purely physical 
laws." Or we contradict ourselves, and then call the 
result a " Mystery," or an " Antinomy of Reason," wash- 
ing our hands of all responsibility, and content to lay it 
on the Powers that designed the faulty human intellect. 
The humble mind has an easy command of numerous 
humble phrases. 

Practically the surest defence against Scepticism lies, 
not in claiming infallible revelations, but in patiently 
making the best of the truths that have stood the test 



316 FALLACIES. [Part II. 

of time. Not, of course, only the few that exist now in 
the shape in which they were originally put forward, but 
also the many that have been gradually narrowed down 
and pared into lasting shape by persistent hostile forces. 
On these we 'ancients' build, as on a basis always 
growing firmer : — though in recognising the fact, we of 
course admit that our basis is never completely firm. 
But just in this recognition lies the life and strength of 
science ; for the admission gives a power to discover and 
correct mistakes, and also tends to weaken the natural 
petty desire to pose as supernaturally knowing. Free 
from the fear of being found an impostor, science is 
able to challenge — and to court — correction: more than 
it loses in influence by being proved mistaken, it gains 
by being known as honest, and it adds a further gain by 
registering the mistake. Knowledge is built upon a mass 
of prejudices, possibly, but one difference between scientific 
and unscientific prejudices is that the former are chiefly 
recognised as provisional merely. If it were not for 
these strong provisional prejudices, Science would hardly 
have reached the results already won. Until they prac- 
tically fail these may be trusted, and where they are 
proved in any case fallacious we only learn a further 
piece of knowledge, and so really add to, not weaken, 
our old foundations. Logic is fond enough of reminding 
us that "All men are fallible:" but the rider must be 
added that it depends largely on ourselves to say to 
what extent we choose to live under the sway of fallacy. 
And as to unpractical hesitation, again we may appeal 



Chap. VHL] SOME OBJECTIONS TO LOGIC. 317 

to results. It is easy of course to assert that these have 
been reached by Common Sense in spite of Logic, and in 
one sense possibly this may be true. But that is an 
objection to a name, and not to a process : whether 
' logic ' or not, it is consistency of thought, deep analysis 
of supposed simple phenomena, and recognition of possible 
unknown antecedents, to which the results have been 
mainly due. To refuse all belief until we reach absolute 
demonstration would of course be an unpractical habit ; 
but between doing this and merely recognising the 
possible loopholes of error, there is all the difference that 
exists between standing still and moving cautiously. 

It is clear too that these more fundamental objections 
to careful inquiry would come with greater force if they 
were once for all to declare their exact position unmis- 
takably. At present they are apt to shift their ground 
too fast to hold it firmly. Science finds itself between 
two apparently contradictory objections, both often 
coming from the same objector, — that it is too dogmatic, 
and also not dogmatic enough. Either on the whole, or 
on any given point, one or other of these charges may be 
true ; but it would at least tend to enable us to correct 
our errors, if the charges were to cease to destroy each 
other. 

A more insidious form that this objection to Logic, 
and defence of Fallacy, sometimes takes, closely resem- 
bles the attitude of loose, good-humoured Optimism 
towards the problem of Evil. Since Fallacy is a fact in 

Nature, let us recognise it as part of the wisely-ordered 
15 



318 FALLACIES. [Part II. 

scheme of tilings, without which Nature would be 'in- 
complete.' To hold it merely for an enemy is 'narrow* 
and 'one-sided/ Or let us view it, at the lowest, as 
useful manure to raise the crops of reason. Nearly all the 
more important theories we possess have been preceded 
by a number of false ones, and without the latter the 
former could never have been attained. Only the slug- 
gard never commits a fallacy. A touch of madness is 
usually found along with the highest genius, and no one 
is good for much who lacks a spice of the fool. 

This is, of course, an unduly brief account of the view 
here spoken of; and it is eminently a view that will 
hardly bear so definitely stating, but needs as much dilu- 
tion as possible Perhaps, however, it will serve to show 
what is intended, more especially as the statement given 
above does mix up — just as the easy optimists commonly 
do— two quite distinct, and mutually destructive, de- 
fences, neither of which would be found so satisfactory 
by itself. The first of these, — that Fallacy is a part of 
our total nature, and therefore worthy of our respect, 
rests on a merely verbal confusion, and one which no 
man has ever yet quite been able to preserve consistently. 
If Fallacy is a part of our nature, so, surely, is the power 
to recognise Fallacy as unprofitable, and the wish to 
avoid it as far as we can. There is hardly any element 
of human nature really stronger than the wish to dis- 
criminate between truth and erroly)— except perhaps the 
wish to keep the still wider distinction of good and evil 
clear. While we are about worshipping our instincts, 



Chap. VIIL] SOME OBJECTIONS TO LOGIC. 319 

why neglect the most fruitful and persistent of them all ? 
That the view has a certain charm, over and above the 
mere refreshing effect of the paradox, will be readily 
admitted by most people. It is often a great relief, and 
sometimes has a healing and strengthening effect, to feel 
free to relax our wakefulness a little. But the thing can 
be very easily pushed over into an absurdity, — or, what 
is worse, can be accepted as a serious theory by minds 
that might otherwise have kept or attained some vigour. 
To yield to it to any great extent is as enfeebling to the 
mind as long-continued sensuous luxury to the body : 
the comfortable sentiment, "I am sufficient as I am," 
may be of use now and then as a piece of rather open 
self-deception, but a mind that truly and firmly held such 
belief for any considerable length of time would miss the 
bracing effect of a struggle for improvement. 

The second defence, — that error often leads to truth, 
— has this advantage over the first, that it does preserve 
the distinction between the preferable and the unprefer- 
able. And so long as this is clearly and consistently 
done, I do not see that we need at all object to recognise 
the fact. But this is certainly no argument for remaining 
in an error longer than we can help. By all means admit 
that liability to error is part of the price we have to 
pay for forward movement ; but are we to pay the price 
and then contentedly forget to carry home the purchase ? 
The transaction needs again to be viewed from both sides 
instead of from one only. Rather than stop short at the 
fact that fallacy has its uses, we need to remember that 



320 FALLACIES. [Part II. 

it is only justifiable when it has really led to the good 
results ; and this is apt to be sometimes forgotten. 
There is, however, one purpose for which the view in 
question seems to me to have considerable value, and that 
is, to force us to see that a man who commits even a 
large number of fallacies is by no means necessarily a 
fool. I do not mean that this is an advantage only so 
far as it leads us into charity towards opponents, but 
also, and chiefly, that it tends to weaken the weight of 
mere authority as regards any given question: a man 
may have all the wisdom and learning of an Aristotle, and 
yet be quite mistaken on a given important point. The 
recognition of this fact tends to make us value conclusions 
more on their own merits and less on the merits of those 
who advance them. 

Such, in rough outline, are the chief objections of 
this class. On the whole, I think we may say, that when 
viewed as mere protests against the opposite extreme, 
they often have a value. But they are too seductive in 
themselves, too gratifying to common vanity, and too 
open to employment as simple excuses for idleness, to 
remain always in their proper place, and as a rule their 
professed exponents appear by no means conscious of 
the needed limitations. 

As regards the objection that Logic is too slow and 
clumsy to be of the highest practical service, there seems 
little to be said, except to admit the fact, and even 
to urge it as a reason for doing all we can to improve 
the methods of fighting fallacy. It seems undeniable 



Chap. VIIL] SOME OBJECTIONS TO LOGIC. 321 

thafc there is an artificial rigidity about all definition, a 
false simplicity about analysis, a standing failure in all 
attempts to cram the universe into labelled nutshells. 
Where Proof depends on many intricate special circum- 
stances taken together, the analytical habit of mind may 
often be disastrous. There are plenty of valuable 
facts too shadowy for Proof, and plenty of occasions 
where, if we had to wait for logical investigation, the 
opportunity would be gone, — "there being," as Bishop 
Warburton expressed it, " no worse practical men than 
those who require more evidence than is necessary." If 
common sense is rough, Logic, at least, is far from ready, 
and sometimes its pretended deeper insight is practically 
either futile or misleading : for Logic is bound by 
language, and language always hangs a little behind 
the newest glimpses of truth. 

The facts being admitted, it is much easier to find 
this fault with any existing system of Logic than to 
supply a better system : and if the objection were 
brought solely, or mainly, by those who know something 
of the difficulties to be encountered, every one who cares 
about the matter would welcome it gladly. Unfortu- 
nately this cannot be said to be the case. The alterna- 
tive everywhere suggested by these objectors is one 
which growing experience has always been steadily 
finding, on the, whole, untrustworthy. Whether we call 
the alternative(^coinmon sense * or ' intuition,', its fault 
is the same, — that, where it really exists, it is so truly 
a better instrument than slow and deliberate reason, 



322 FALLACIES. [Pakt II. 

that people are apt to claim, or to imagine, they 
possess it, when they really possess it not. It is open to 
any lunatic to know by intuition that he is the angel 
Gabriel, just as it was formerly open to common sense to 
see that the Sun went round the Earth, or to feel that 
the Antipodes were a plain absurdity. 

In the face of omnipresent illusion, and of possible 
lunacy, it seems that we must often be content to sacri- 
fice speed, at least, in the attempt to get the most objective 
standard possible. Whether breadth of view need really 
be sacrificed depends chiefly on the time at disposal in the 
given case, partly also on our power of employing highly 
general words or symbols. But what is here contended 
is, that whatever be the sacrifice required, it is safer to 
make it than to imagine the other alternative really pre- 
ferable on the whole. It is not claimed that whenever we 
are called upon to reason we shall gain by deliberately 
reducing the process to formulas. But what is claimed 
is that unless we have the power to do so, we have 
nothing else to keep our reasonings straight. There are 
two distinguishable states of mind in which slow and 
deliberate reasoning is now and then dispensed with, — 
one the reasoned belief that in a given case, or set of 
cases, it is better to trust to rapid insight, doing this, 
however, with all the care available and with a clear 
recognition of the danger ; and the other, the far com- 
moner state of mind, composed partly of mere easy-going 
ignorance of the difficulties, partly of dim and floating 
views of important truths, and largely perhaps dependent 



Chap. VIIL] SOME OBJECTIONS TO LOGIC. 323 

on more purely physical conditions. These are, at least, 
the two ends of the scale : no one is, quite consistently, 
either an angel or a fool, either a doubter or a seer; 
and even the man who follows his ' moods ' has a 
reasoning mood amongst others. But still we may class 
men broadly in two opposite camps, according as, on the 
whole, they are for or against the deliberate use of 
reason. In the former case, we occasionally make a 
compromise and voluntarily accept what seems to us 
in the special instance the smaller of two evils ; in the 
latter case, — and hence, no doubt, its popularity, — we 
know little or nothing of evils or of danger, but 
merely glow with faith in our penetration, and with 
honest anger at any attempt to call the results in 
question. If, as so often happens in the latter case, we are 
also gifted with eloquence, it lies in our power to do 
much harm to those who have not yet declared for either 
side. It is easy enough to paint Insight in florid and 
striking colours, Reason as cold and dismal: and the 
weaker brethren are always glad of a powerfully phrased 
excuse. 

There is, no doubt, much to be said against the 
careful employment of reason; but it is not the whole 
story, nor even the most important part of it. The 
practical problem is, how to make use of logic without 
spoiling our common sense, or how to make use of our 
common sense with rather less common discretion. Im- 
patience with logical method may no doubt here and 
there be justified, whether in Philosophy or in looser 



324* FALLACIES. [Part II. 

regions of thought ; but far more often it is merely an 
expression of the unchecked desire to run before we 
have learnt to walk. Here and there it is plain that the 
impatience springs from a genuine wish for improve- 
ment in our methods, but far more often it flows either 
from idleness or from being unaware that there are 
any methods to improve. And in any case, though we 
may appreciate the good intention shown, as yet the 
fruits are wanting. If logical method as at present 
known is insufficient, the sole alternative is unmethodic 
speculation, which on the whole is less sufficient still. 
It is open to any one to sit down and dream that to him 
alone has been given the key of all knowledge — or of 
any given piece of knowledge, — without any laborious 
precautions. And perhaps he may be right. But how 
is he, after all, to be sure of this on reflection, and 
how are his friends to know it, and the other people 
with different dreams of their own ? Whether the seer 
needs an objective standard or not, he will hardly deny 
that rival seers need one : and in their case, at least, he 
finds, just as the scoffers do, that the calm security of 
inspiration is difficult to distinguish from a child's 
untroubled conceit. 



CONCLUSION. 

SUMMARY. 

To challenge attack is of the essence of ' real ' assertion, 
and the kind of challenge depends on the confidence 
with which the assertion is made. Sometimes we speak 
as having fully considered the question ; sometimes as 
rather waiting to hear, as a novelty, what may be said 
on the other side. It is with the former case only that 
we have been here concerned, and for convenience in 
describing this kind of assertion we have employed the 
ancient name of Thesis. 

The first of the dangers that a Thesis has to run, we 
found to be that of containing the empty form of asser- 
tion without the substance. If no real meaning be 
understood by the hearer, to him the thesis is non- 
existent, whether for acceptance or attack. And the 
hearer alone can decide how far the meaning is real. 

When the meaning is real and clear — or sufficiently 
clear for its purpose — the second danger is that of sup- 
posing that a thesis, to be left unaccepted, stands in need 
of Disproof. And here the distinction between Disbelief 



326 FALLACIES. [Part IL 

and Unbelief is all-important : or, however the states of 
mind be named, the thing to remember is that so long as 
a thesis is unsupported it has not yet been shown to be 
either true or false ; that although it claims to be true, its 
claim is not yet made out. The attempt to support an 
assertion by asking what can be said against it, may be 
met by replying that at present we know nothing against 
it, but this much against accepting it — that we see no 
reason to believe. He who asserts may choose between 
the two alternatives — producing reasons to satisfy the 
inquirer, or leaving him unconvinced. 

And lastly, when reasons are brought forward, the 
question at once arises, how far the proof comes short of 
being conclusive : or what are the gaps remaining before 
Demonstration is complete. And having found these (as 
they appear to the inquirer), the safe and fair attack is 
still to ask for information : not necessarily to accuse the 
assertor of absurdity ; only to force him to take care that 
he in fact avoids it. 

But to view the office of Logic as consisting purely in 
sceptical attack, is itself a kind of artifice, undertaken 
with a far more useful purpose in view. It is not the 
seizing of firm positions in verbal controversy that is the 
chief aim of logical method, but the power thus gained 
may be used as a means to a further end. Since a priori 
any belief may be erroneous, and especially since we 
have already often found ourselves and others mistaken, 
there is a certain use in learning to treat ourselves as the 
wary debater would treat a less wary opponent. The 



Conclusion.] SUMMARY. 327 

attack on any erroneous belief must come either before 
or after its acceptance has led us into actual error. The 
practical purpose of Logic is to enable us to forestall the 
possible attacks, and so to guard against the consequences 
of credulity. Logic thus aims at the adoption only of 
those beliefs that cannot fairly be avoided, and its opera- 
tion is in the first place mainly to restrict the natural 
exuberance of belief. 

It is not necessary here to repeat in any completeness 
of detail all the separate points of doctrine on which the 
science of Logic depends : nor can I, indeed, pretend to 
be able to sum them up in the most concise available 
form. Apart from metaphysical difficulties, the latter 
operation would demand both a wider symbolic language 
than is at present accepted, and also a more universal 
practice of handling symbols easily and reading their 
application. Expressed in more highly general language 
than we have, the logical doctrines that are of chief 
importance from the practical point of view would prob- 
ably be few in number, simple in nature, far-reaching in 
their application, and true under all conditions of their 
use. Such as we have already are, when wrongly inter- 
preted, open of course to easy caricature — as every pun and 
every verbal puzzle bears witness : but, interpreted fairly, 
we need never be afraid of trusting our weight upon 
them. Like Science in general, Logic exists for a pur- 
pose, and wherever it fails to attain that purpose the 
failure merely needs incorporation into our statement of 
its laws. Thus we may use, for example, the law of Con- 



328 FALLACIES. [Part II. 

tradiction, while fully admitting that the line between A 
and not-A is a contrivance of our own : or we may use 
the Reduction to Absurdity while recognising that it only 
asks a question. But without attempting here to draw 
up the list of doctrines, it may be of use to select as land- 
marks for memory some of the salient features of the 
science. 

The first of these I hold to be the negative attitude 
above spoken of. And the second, all that is included 
under the name Consistency. As already shown, this 
contains much more than what is commonly meant by 
' abiding by our assertions/ namely the whole problem of 
bringing to light the hidden implications underlying a 
thesis, and especially the large assertion implied in every 
confident theory — that all possible conflicting theories are 
to be discarded. That this demand, if strictly enforced, 
would be a bar to all belief, may be freely admitted. 
What Logic is concerned to do is, not to remove all 
theoretical doubts, but to force us into recognising as 
clearly as possible their actual extent and power in the 
given case. As a first means of pointing out the dangers, 
it sets up an ideal type of Demonstration, and then 
demands not that we shall reach this but that we shall 
know clearly how far short of it we fall: for it finds 
that until the distinction between proven and not-proven 
is apprehended with some real distinctness, there is no 
chance of dealing successfully with the endless complica- 
tions due to varying degrees of strength in evidence. 
The more we inquire into the main sources of error, the 



Conclusion.] SUMMARY. 329 

more clearly we see that ignorance of danger is at once 
the commonest and the only one that we can certainly 
remove. Hence the central purpose, for practice, is to 
find the gaps in Proof remaining to be filled. 

The definable term, the abstract proposition, and the 
argument, have this in common, that each is capable of 
being viewed as expressing an indication. Given the 
general name, and any of the essential attributes follow ; 
given the S of an abstract proposition, and the §j follows ; 
given the Reason and the Thesis follows. And to each 
of the three the rule of counter-indication applies : deny 
an essential attribute and we deny the name ; deny §5 
and we deny S; deny the Thesis and the relevant 
Reason is denied. 

In the attainment of Consistency the Law of counter- 
indication has two chief uses ; first that of restraining us 
from taking two distinct assertions as equivalent, and 
secondly as a means of helping to bring to light the 
hidden implications. In the former, or negative, aspect 
it operates chiefly by preventing us from proving some 
easy proposition under the belief that we thereby prove 
its reciprocal also. In the positive aspect the chief value 
of the law is in helping to explain the syllogistic process. 
But such explanation demands — 

Next, the assumption that every isolated fact comes 
under a wider law. This doctrine lies at the root of 
Proof and of Explanation equally. To prove a thesis, 
we need to show it as a case under some Principle — 
just as, to explain a name we have to mention a genus, 



330 FALLACIES. [Part IL 

or as to explain a fact we have to bring it under a law. 
And of that Principle the thesis may be either a denial 
of the antecedent (S), or an affirmation of the consequent 
(§b) • while the Reason either denies the consequent or 
affirms the antecedent. By means of Thesis and Reason 
together we can thus find the law implied. 

Lastly, there is the doctrine that every isolated fact 
is further analysable — that besides belonging to a genus, 
it possesses also a specific difference. And that, in order 
to view such fact correctly we need to bear its differential 
qualities in mind. The eye for genus thus leads us to 
attempt to establish our thesis deductively, while the 
eye for differentia becomes the main safeguard of 
induction. While, then, we continue to assume, as 
a basis for practical proof, that all ' things ' belong 
to classes, the names of which may be used as in- 
dicating certain facts about them, Inductive Logic 
teaches us to cultivate the eye for difference, — to keep 
refining away what passed at first sight as indivisible, 
and breaking down ancient barriers that perhaps have 
served some useful purpose but were better suited to 
clumsier needs than ours. Deductive Logic insists that 
conclusiveness depends on indication, — the trustworthi- 
ness of laws ; inductive Logic leads us to revise the laws 
themselves, and put us on guard against accepting them 
too widely. The power of seeing finer shades of differ- 
ence is on the whole the best and most lasting result 
of logical training, and affords most help in the rapid 
detection of fallacy. 



Conclusion.] SUMMARY. 331 

These seem to be, in briefest outline, the more im- 
portant points to keep in mind : but as thus shortly 
stated they can only be of use as memoranda, not as in 
themselves by any means sufficient statements of all that 
is required for practice. Nor, certainly, would such 
sufficient statements be easy to frame. It is not theory 
alone that can ever fully enable us to preserve the golden 
mean between faith and hesitation. So commonly is 
this fact recognised, however, that it will be well 
if we can avoid going far beyond it and accept- 
ing the easy view that Theory and Practice must 
for ever carry on a hopeless warfare, and that, so 
often as our weak attempts at theory fail to fit 
the facts, it is sufficient to plead the possession of a 
highly practical spirit. Perhaps one chief source of 
difficulty here is the habit of supposing that Logic wishes 
to dictate instructions for belief, — saying, for example, 
" This you may consider sufficiently certain, but that 
you shall not accept." No logic can really lay claim to 
so supreme an authority. It is wiser to admit that men 
are perfectly free to form their beliefs, if they choose, 
with the aid even of self-deception. The most that Logic 
can hope to do, for practice, is to help us to know the 
dangers of uncriticised belief; it is entirely our own 
concern if we afterwards prefer, in a given case, to disre- 
gard them. The risks however remain, whether we care 
to remember them or not. 



APPENDIX. 

A.* 

ALTERNATIVE POSSIBILITIES. 

As a help in recognising the alternative theories against 
which any abstract proposition has to show its preferability, 
there may be some use in setting out the a priori possibilities 
between S and j& in general. 

We must remember that S and §b are abstracted portions 
of the total phenomena among which they respectively occur; 
portions selected and named by ourselves, for the purposes 
of our ' general knowledge : ' the actual phenomena observed 
being complex wholes, mentally analysable into this that 
and the other circumstance, whether such circumstances be 
events or qualities. It should be observed, however, that 
when successive phenomena are in question these abstracted 
portions may always themselves be viewed as ' events,' even 
where so uneventful as hardly to deserve the name in popular 
language. Thus, where any quality of any thing changes 
ever so slightly, — say when a thermometer rises one degree, 
— we have what is here considered an ' event/ even though 
a caterer for news might hardly think it worth reporting. 
And the abstractness of such an event consists, as abstract- 
* See p. 276. 



334 APPENDIX. 

ness always consists, in its detachment from surroundings : 
we choose to keep out of our assertion (and as far as possible, 
out of sight) the whole environment of S and of j£, and to 
speak of these alone, labelling them with general names. 
For example, let S be a rise in the price of coals, and j& 
a strike among the colliers. Outside S and j*, and simul- 
taneous with them, is a whole universe of other events 
and qualities, too numerous to sum up by any narrower 
expression than their * environment : ' these we, by a sort of 
fiction, choose to neglect, attending only to S and j&. 

And first, when S is observed to happen earlier in time 
than j£ ; if we inquire as to the various ways in which these 
may conceivably be related to each other in Causation, we 
find:— 

First S may be cause of jc : — 

(1) as what is often loosely called the sole cause. That 
is, if S had not happened, Jd would not have 
happened; all other circumstances in S's environ- 
ment being * accidental ' to j& : as where S is the 
passing of a bullet through a healthy man's brain, 
and jd the death of the man. 

(2) S and a third circumstance, Z, may have been 
jointly essential to jb's happening. That is, without 
their combination, j& would not have happened : as 
where Z is a certain person's weak state of health, S 
is the arrival of fever-infection, and jr> his consequent 
fever. 

(3) S and Z may have jointly contributed to j&'s ex- 
istence, without their combination being essential to 
the production of j& at all. That is, witbout one of 
them, j£ might have happened, but not to so great an 
extent or intensity : as where S and Z are a pair of 
horses, and j& the movement of the carriage. 



ALTERNATIVE POSSIBILITIES. 335 

(4) S may have been itself due to a former case of je, 
but may now be in its turn cause (whether sole or 
otherwise) of the present j£ : as where S is a rise in 
the bank-rate, and j& a general uneasiness in the 
money-market. 

Secondly, S and jfc may be co-effects of Z : as where S is 
day, j£ is night, and Z is the earth's revolution in 
the sunlight : or where Z is a ' centre of depression,' 
S is a falling barometer, and jc a storm. 

Tltirdly, Z may have been (sole or other) cause of jc, and 
S accidental: — 

(1) Simply accidental, as where S is the act of blowing, 
j& is the flying open of the watch-case, and Z is the 
pressure of my finger on the spring. (Along with 
this may be classed the case where Z is the effect of 
S, and jc accidental : as where S is the arrival of a 
comet, Z a letter in the Times about it, and j& a 
war.) 

(2) Z may have been the cause of jj, and S a hindrance : 
as where j& is the flourishing state of trade in 
America, Z is the 'boundless resources of th6 
country,' and S is the system of Protective Duties. 

Looking next at the case of Co-existence, we shall find in 
the first place that unless S and £ stand merely for qualities 
(or groups of qualities), and not for events, it will be very 
difficult to find examples of true co-existence with direct 
dependence between S and jfc. In other words, where S and 
j& are two co-existent events, say where S is the arrival of a 
train at the station, and jd the arrival of the clock's hands 
at a certain position ; or where S is a gale and j& the move- 
ment of the branches of a tree ; the case is always more or 
less plainly resolvable either into one of co-effects, or else of 
innumerable repeated acts of causal sequence. As to co- 



336 APPENDIX. 

effects; if it be true that every event whose beginning we 
can trace has had a cause, and also that any selected portion 
of continuous Nature that we choose to consider separately 
may be bound up into a single ' event/ it is clear that the 
relation itself of co-existence between S and j& may be con- 
sidered as an event, and therefore as having a cause. And 
thus, unless the whole assumption on which our explanation 
of Nature proceeds be unfounded, every case of co-existence 
is, strictly speaking, a case of co-effects. We have only to 
trace back the chain of causation far enough, and sooner or 
later we must come to an ancestral event common to both. 
But this fact, however undeniable, is of small practical value, 
since the interests of practice require above all things a dis- 
tinction between the cases where S and Jd are essential to 
each other and where they are accidental. And the sweeping 
general assertion made above cannot be held to deny the 
apparent (and therefore practically existent) disconnection 
between many cases of observed co-existence. The falling of 
a cab-horse in Cheapside may co-exist with a particular 
storm at Penzance (to go no further afield), and if we knew 
all the links no doubt we should be able to trace both events 
back to some ancestral cause, however inconceivably exten- 
sive and complex. The horse, let us say, would not have 
fallen unless the street had been wet, and this occurred 
because certain rain drops had come down in that par- 
ticular place and time : the falling of the rain depended 
on certain atmospheric collocations and changes, and these 
again on others in an endless series where we soon lose all 
actual clue. But our whole theory of causation demands 
that at some time or other in the past, however remote, a 
change, or group of changes, took place, to which both 
the Penzance storm and the Cheapside accident are due, 
— without which neither would have happened exactly 



ALTERNATIVE POSSIBILITIES. 837 

as and when they did happen. This seems certainly 
demanded as a theoretical assumption : and yet, for all 
practical purposes, the two events in question were ' totally 
disconnected.' Just as, practically, there is such a thing as 
* Chance,' so must we admit that many cases of co-existence 
are * purely accidental,' or * mere coincidences ; ' even if this 
means only that we have no definite knowledge of the actual 
chain of causation involved. 

And as regards the case of innumerable repeated acts of 
causal sequence, — as where, for instance, a stream runs on for 
ages and slowly polishes a rock, — the flow of the water may 
be said, in rough ordinary language, to co-exist with the 
wearing of the stone, but the process can also easily be 
analysed into infinitesimal acts of removal of particles by 
abrasion, — the effect in each case coming after its cause in 
time. In fact, in one sense, any other explanation is incon- 
ceivable. Here again we have a case where theoretical 
assumptions clash with the practical needs of expression; 
and where, as it seems, our only resource is to yield to the 
latter. While admitting then that, strictly interpreted, 
co-existence is only of qualities, which are always co-effects 
of some prior cause; we must be content with a looser 
form of expression, and speak of co-existent events also, 
one of which may be either essential or accidental to the 
other. 

Of co-existent events then, the conceivable cases follow 
closely the division above made of successive events, 
namely : — 

First, either may be the cause of the other : — 

(1) Sole cause ; e.g. S the forward movement of a train 

and 5b the rotation of the wheels. 

(2) Joint essential; e.g. S the force of Gravity, j& the 

fall of an apple, and Z the absence of support. 



338 APPENDIX. 

(3) Joint contributing ; e.g. S a large river,* £ a large 

town upon the river, and Z the other causes of the 
size of the town. 

(4) Reactive; e.g. S reason, and j& language. 
Secondly, S and js may be co-effects of Z. E.g. S a low 

thermometer, j& the formation of ice, and Z frosty air. 
Thirdly, the conjunction of S and j& may be ■ purely acci- 
dental ' (i.e. S the effect of Z, and £ of X.) 

(1) Simply ; e.g. S fine weather and j& Koyal review. 

(2) Obstructively ; (either existing in spite of the other). 

E.g. S liberty of the press, and j& the spread of 
foolish theories. 
Of co-existent qualities, only three cases need be distin- 
guished : — 

(1) S and je essential f to each other. (This case is rare.) 

E.g. S inertia, and j& weight. 

(2) j& essential | to S. 

E.g. S human nature, and jfc fallibility. 

(3) j£ accidental to S. 

(a) Simply; 

E.g. S shortsightedness and je short stature. 
(/?) Obstructively. 

E.g. S disregard of wealth, and j& possession of 

wealth .{ 
Seeing then that when events or qualities are observed to 
happen in succession or co-existence, there are a priori these 
various explanations possible, how are we to rise from the 

* It may seem strange to call a large river or a large town 'events,' 
but here the names are only used elliptically, for the growth of the town 
and the continued existence of the river ; so too in the other cases. 

f By ' essential ' is here meant no more than ' constantly accom- 
panying,' and therefore ' indicated.' 

X This further exemplifies the difficulty noticed on p. 335, that 
causation is sometimes so subtle as to wear the appearance of co- 
existence. 



THE EMPIRICAL METHODS IN DETAIL. 339 

observations or experiments made, to the laic of succession or 
co-existence obtaining between the things ? I do not mean, 
by what method are we to direct our guesses so as to be 
most quickly successful ; but how, having made a theory, are 
we to prove it ? 

It will be seen, of course, that these alternatives just set 
out are alternatives which affect our explanation of each 
single observed case of sequence or co-existence. But since, 
in order to prove a concrete proposition satisfactorily we 
must always have at least one abstract proposition to rely 
upon, the whole importance of these alternatives is as regards 
the proof of abstract propositions from concrete facts observed. 
Before considering a law established, either by one or by 
many cases of observed sequence or co-existence, these alter- 
natives have to be faced, as possible explanations of each 
case observed. And the immediate question in each case is, 
What certainty can we obtain that the alternative chosen is 
the right one out of all those conceivable ? The methods of 
inductive proof may be viewed as attempts to answer this 
question. 



B.* 

THE EMPIRICAL METHODS IN DETAIL. 

As Mill pointed out, the five methods — Agreement, Joint- 
Method, Difference, Eesidues, and Concomitant Variations 
— exemplify at bottom two methods only, Agreement and 
Difference, the Joint Method being merely an extension 
and improvement of the Method of Agreement, the Method 
of Eesidues being a peculiar modification of the Method of 
Difference, and the Method of Concomitant Variations being 
* See p. 278. 



340 APPENDIX. 

an approach to the Method of Difference, the nearest approach 
attainable in certain circumstances. There are, then, two main 
axioms at the foundation of all the methods ; the first, that 
whatever circumstances can be excluded without excluding 
the phenomenon whose effect (or cause) is being sought, or 
can be absent notwithstanding its presence, are not causally 
connected with it. According to this rule, accidental circum- 
stances are gradually eliminated by observation, and the more 
observations the greater the chance that the truly accidental 
circumstances will be excluded. The remainder, those cir- 
cumstances which are not eliminated by this process, are 
supposed to be thus shown to be essential to the phenomenon, 
to be the proved effect (or cause). As a concise example, we 
may quote from Professor Fowler, " A particular kind of food, 
whatever else I may eat or drink, and however various my 
general state of health, the temperature of the air, the 
climate in which I am living, and my divers other surround- 
ings, invariably makes me ill," [let us say rather * is invari- 
ably followed by my illness '] ; "I am justified in regarding 
it as the probable cause of my illness, and avoid it accord- 
ingly." Here the general state of health, the temperature, 
and the other surroundings, are the circumstances gradually 
eliminated, by the observations, as immaterial; and it is 
supposed that the only circumstance (except an uncertain 
number of circumstances already believed to be immaterial) 
common to all the instances observed, and thus surviving 
the process of elimination, is the * particular kind of food.' 
So far, then, as the method of agreement is to be trusted, this 
particular food is proved to be the cause. We may guarantee, 
says the Method of Agreement, by means of the observed 
facts, the abstract proposition, " This particular kind of food * 
(S), whenever taken, indicates future illness in me (je)." 

The second axiom, on which the Methods of Difference, 



THE EMPIRICAL METHODS IN DETAIL. 341 

direct and supplementary, are based, admits of a two-sided 
statement : " Whatever antecedent cannot be excluded with- 
out preventing the phenomenon, is the cause, or a condition, 
of that phenomenon : whatever consequent can be excluded, 
with no other difference in the antecedent than the absence 
of a particular one, is the effect of that one." * Chemistry is 
one of the best fields for illustration of this method. " Mix, 
for example," says Prof. Fowler, " chloride of mercury with 
iodide of potassium, and the result will be a colourless liquid 
at the top of the vessel, with a brilliant red precipitate at the 
bottom. There can be no hesitation in ascribing this result 
to the mixture of the two liquids." The assumption of course 
always is, where a change introduced into a given set of cir- 
cumstances is immediately followed by a further change, that 
without the first change the circumstances would have re- 
mained as they were, that the second change would not have 
taken place. Thus, in the instance given, from the chloride 
of mercury alone, without the iodide of potassium, no red 
precipitate (it is assumed) would have been formed. The 
iodide of potassium is accordingly an "antecedent which 
cannot be excluded without preventing " the phenomenon 
observed : the consequent 'red precipitate' can be excluded 
with no other difference in the antecedents than the absence 
of the iodide of potassium. So far, then, as we may trust to 
the Method of Difference, . we reach the law "Chloride of 
mercury added to iodide of potassium — > red precipitate." 
We will not ask how far these methods, and the subordi- 
nate variations of them, can be trusted for proof of absolutely 
universal laws of sequence, whether of backward or of for- 
ward reference, — laws, e.g., such as " Wherever S is found, 
je must have been before," or " Wherever S happens, <§? is 
sure to follow." Practically, as already said, we are for the 

• Mill's Logic, vol. i. p. 450. (8th Ed.) 
16 



342 APPENDIX. 

most part obliged to be content, in our knowledge of causal 
sequences, with much less than these completely universal 
assertions. The mass of our propositions regarding causal 
laws are of the milder type, " j& is one cause of S," or " S, 
unless counteracting circumstances interfere, will cause j& to 
follow." It is necessary, therefore, to inquire how far the 
empirical methods may be relied upon for the support of 
such comparatively timid assertions as these. 



The Method of Agreement, 

Canon. — If two or more instances of the phenomenon under 
investigation have only one circumstance in common, the circum- 
stance in which alone all the instances agree is the cause (or effect) 
of the given 'phenomenon. 

It is obvious, in the first place, where the simple Method 
of Agreement fails. Its ' characteristic imperfection/ as 
Mill himself took care to show, is due to our necessity of 
admitting that the ■ same effect ' may be produced by * dif- 
ferent causes.' Of course, as Mr. Carveth Read puts it, an 
effect particularised to the full can never arise from different 
causes ; but the very essence of these abstract propositions 
is that they particularise to the full neither S nor jfe, and so 
far as they fall short of describing an effect " in the minutest 
detail," so far they leave an opening for vicarious causes. 
The manner in which the vicariousness (* Plurality ') of 
causes interferes with the cogency of the method is easily 
seen. Assume, for instance, that I have made ten observa- 
tions as to the apparent ' effects' of eating salmon ; having ten 
times observed this antecedent to be followed by indisposi- 
tion. On each of these occasions there have been many other 
circumstances combined with it, — the other things eaten and 
drunk during the same period, to go no further. In order to 



THE METHOD OF AGREEMENT. 343 

put the most favourable case possible for the operation of the 
method, we will also suppose that the salmon was the only- 
antecedent common to all the cases of indisposition. But if 
vicariousness of causes be once admitted possible, there is 
nothing to prevent A having been the real cause on the first 
occasion, B on the second, C on the third, and so on ; S (the 
salmon) having been perfectly harmless all the while, — just 
as harmless as some other circumstance which, though not part 
of the food, is invariably present in all the cases, — say the 
fact that Bismarck is still alive. Unless, in short, we have 
some further reason to suspect the element in question to be 
the guilty one (in the case supposed, e.g., we may rely on 
popular belief, or doctor's advice, or family tradition) — un- 
less we can bring deduction from some accepted truths to aid 
us, the mere method of agreement by itself can give, in such 
cases as these, no solid support at all. 

There is, however, it will perhaps be said, one class of 
cases in which the unsupported method of agreement must 
be allowed to be practically sufficient; namely, where the 
cases observed are not counted by tens, but by hundreds or 
thousands or more. But putting aside the difficulty of set- 
tling where the sufficient number begins, and also the diffi- 
culty of finding an unmistakable instance of such a case, — 
for where the observations are numerous either the joint 
method or that of concomitant variations is usually appli- 
cable,* — what is there to prevent these thousands being all 
under the same limitation ? " We might," as Mr. Fowler says, 
" pass through a field containing thousands of blue hyacinths, 
but this would not justify us in expecting that the next time 
we saw a hyacinth it would be a blue one " [say rather, * this 

* Certain axioms, e.g., sometimes quoted in this connexion, seem to 
me to be more dependent on concomitant variations than on strict and 
mere agreement. 



344 APPENDIX. 

would nut prove that all hyacinths are blue ']. A large 
number of minor differences may be thus eliminated, and yet 
some important limitation may remain so as to constitute a 
differentia common to all the cases observed. In other words, 
besides mere number we need the assurance that these in- 
stances are fairly representative of all that exist. The 
field of our observation may be a large one, but there may 
also be other fields outside of it, — until such possibility is 
excluded. 

The Joint Method. 

These difficulties are partly met by the Joint Method, 
but not entirely. The Joint Method compares two sets of 
instances independently, and combines the results. Its 
canon is, in Mill's words : — 

If two or more instances in which the phenomenon occurs have 
only one circumstance in common, while two or more instances in 
which it does not occur have nothing in common save the absence of 
that circumstance ; the circumstance in which alone the two sets of 
instances differ, is the effect, or the cause, or an indispensable part 
of the cause, of the phenomenon. 

The canon itself is axiomatic, but its application is far 
from being secure. To test it, let us suppose the most favour- 
able conditions ; namely, that the instances observed are 
considerably more than two in number. Mr. Fowler again 
provides us with a good example— " I have observed that a 
certain plant is invariably plentiful on a particular soil : if, 
with a wide experience, I fail to find it growing on any 
other soil, I feel confirmed in my belief that there is in this 
particular soil some chemical constituent, or some peculiar 
combination of chemical constituents, which is highly favour- 
able, if not essential, to the growth of the plant." 

It is clear that if the one set of instances agree m 



THE METHOD OF DIFFERENCE. 345 

nothing but the presence of the two circumstances, and if 
the other set agree in nothing but their absence, there is of 
course no room for a vicarious cause. But it is jnst this 
further assurance which lies outside any possible application 
of the canon, and which must be added to it to complete 
its cogency in a given case. To refer to Mr. Fowler's ex- 
ample, we need assurance that besides the chemical consti- 
tuents of the soil no other surroundings are invariably present 
and absent together with the soil, — such as climatic condi- 
tions, for example. A wider experience may always, until 
the contrary be shown, lead to the necessity of qualifying 
(i.e. limiting) the law arrived at. Instead of being simply 

" This plant, in general, > these chemical constituents in 

the soil," the law may be, " This plant, under certain conditions 
(of climate or otherwise), — > these chemical constituents." 
In its simpler form the law remains liable to contradictory 
instances being found on a wider search. 

TJte Method of Difference. 

Canon. — If an instance in which the phenomenon under in- 
vestigation occurs, and an instance in which it does not occur, have 
every circumstance in common save one, that one only occurring in the 
former ; the circumstance in which alone the two instances differ, 
is the effect, or the cause, or an indispensable part of the cause, 
of the phenomenon. 

The Method of Difference may be called the sheet-anchor 
of empirical proof. " It . . . appears to be by the Method 
of Difference alone," says Mill, " that we can ever, in the 
way of direct experience, arrive with certainty at causes." 
Elsewhere we frequently hear of its " rigorous cogency." 

An example has been already given, — an example which 
shows the strength of the method but not its weakness : 



346 APPENDIX. 

when we add iodide of potassium to chloride of mercury, we 
may no doubt be tolerably sure of the substances we are 
handling: inside a test-tube unknown antecedents have small 
chance of entry. 

Granting, however, that this method has a practical ad- 
vantage, in many cases, over the other methods ; and that 
its results are often practically beyond cavil ; on what does 
its certainty depend ? Not, in any way, on the method per se 
but on the fact that in certain departments of inquiry (e.g. 
in chemical experiments) we are fairly in a position to obtain 
the external certainty that all the antecedents are known. 
So far as we can be sure that we vary only one circumstance 
at a time, so far we attain this external certainty : so far as 
we cannot get this assurance the method of Difference is no 
more safe than any other suggestive source of inference. 
"Where, as in a chemical laboratory, we have practically entire 
cjntrol over surrounding circumstances, such as light, air, 
and temperature ; where we can obtain any element, or com- 
bination, we require, in the utmost possible purity and in 
the exact proportion desired ; there is no doubt this method 
may be trusted almost absolutely. But the certainty is due 
to the laboratory apparatus and not to the method of Differ- 
ence by itself. When we come outside these highly artificial 
conditions, and attempt to apply the method of Difference in 
circumstances over which we have no control, we find our- 
selves constantly brought up against the fallacy post hoc ergo 
propter hoc. To show simply that in a given case when S was 
added to existing circumstances j& followed, cannot prove 
that S — > <§?, unless we show at the same time that no 
other alteration in the existing circumstances took place, — a 
universal negative which in practice it is often hard to prove 
even approximately. In all the more complex questions, 
such as those of politics, character, or daily life in general, 



THE METHOD OF KESIDTJES. 347 

firm proof by means of the direct method of Difference be- 
comes nearly impossible. Witness the argument that because 
the addition of Free Trade to England's commercial system 
has been followed by periods of depressed activity, therefore 
the former is the cause of the latter. And the possibility of 
conjuring tricks is perhaps the clearest example that can be 
given of the effects of unguarded confidence in the direct 
method of Difference. When the conjurer produces startling 
effects by apparently insignificant causes, there are ' un- 
known antecedents' up his sleeve or elsewhere convenient, 
whose presence it has been his business to make us overlook. 

The Method of Residues. 

Canon. — Subduct from any phenomenon such part as is known 
by previous inductions to be the effect of certain antecedents, and 
the residue of the phenomenon is the effect of the remaining ante- 
cedents. 

It is seldom that the Method of Residues can, or rather 
need, be employed at all as a method of proof, though as a 
source of inference it has often been fruitful and important. 
Astronomical discovery especially is full of striking results 
obtained by means of it : so, too, certain other departments 
of science. But of attempted proof by means of Residues 
merely, we are rather hampered in finding true examples. 
Mill himself gives no instance of its working, except in 
symbols, and every instance given by Professor Fowler is 
an instance of discovery, not of proof. Most of those given 
by Professor Bain are also cases where suggestive hints have 
been first given by this method, to be verified in other ways. 

Here it is clear at once, even without examples, that all 
must turn upon the exhaustiveness with which the residue is 
narrowed down by the known causes and effects in the case. 



348 APPENDIX. 

The difficulties of the method of Difference are therefore 
here repeated, and are further increased by the fact that the 
required isolation of the phenomena is not actually attained, 
but only seen by the light of imagination. The negative 
instance is obtained by deduction, not by direct experience. 
In the last two paragraphs of Prof. Bain's exposition of the 
method, we obtain what seems to me a valuable hint as to its 
true importance for purposes of proof; namely, that it may 
be employed to prove a negative result, — to disprove some 
supposed explanation by showing that the effects can all be 
accounted for in other ways. Thus, if it can be shown that 
the known forces of inorganic matter, operating in the special 
collocations of organic bodies, will account for the phenomena 
of life without leaving a residuum, the theory of a vital 
force, or vital principle, becomes unnecessary. Such cases as 
this are perhaps those for which the method is most adapted ; 
but here too all turns upon the " if it can be shown." This 
condition, and not the mere fact of employing the method at 
all, is the important matter. 

The Method of Concomitant Variations. 

Canon. — Whatever phenomenon varies in any manner when- 
ever another phenomenon varies in some particular manner, is 
either a cause or an effect of that phenomenon, or is connected with 
it through some fact of causation. 

' Concomitant Variations ' is perhaps the most commonly 
applied of all the inductive methods. Its application, ac- 
cording to Mill, is in proving " the laws of those Permanent 
Causes, or indestructible natural agents, which it is impossible 
either to exclude or to isolate ; which we can neither hinder 
from being present, nor contrive that they shall be present 
alone." And it may be added that in almost all those vague 



THE METHOD OF CONCOMITANT VARIATIONS. 349 

and large assertions so common in daily life, the method of 
Concomitant Variations is continually employed in proof. 
More than this, it seems (as already said) not impossible that 
certain Axioms, such as those of Geometry, find their best 
6upport in this method rather than in the method of Agree- 
ment. The more nearly our actual lines approach paral- 
lelism, or our magnitudes equality, the more nearly do the 
axioms fit the facts observed : the more one set of antece- : 
dent circumstances resembles another, the more do their 
respective consequents agree.* In certain cases such as these, 
perhaps, ' unknown antecedents ' can be shown to be as im- 
probable as a pest of mice to the mounted knight. But even 
here we are never quite secure against their interference, and 
what security we have is, as in all the former cases, gained 
from external sources. 

Good examples, usually given, of the employment of this 
method are to be found in the thermometer and the pen- 
dulum. We cannot deprive a body of all heat, and Ave 
cannot entirely remove the Earth from the pendulum, 
nor the pendulum from the Earth ; but by observing the 
variations we may often obtain a law which is practically as 
secure as if it were really obtained by the direct method of 
Difference. We get abundant evidence tending to show that 
if the direct method of Difference could be applied (which, 
by the hypothesis, it cannot), we should have all the cogency 
which that method could give us. 

We should have all that cogency, but no more. For in 
this case, as in the case of all the other methods, we require, 
over and above the employment of the method itself, a further 
assertion on which its actual cogency in the given case shall 

* Cf. also the use made by the late Prof. Jevons of his principle of 
the " Substitution of Similars," where " likeness or equivalence " is 
treated as purely a matter of degree. 



350 APPENDIX. 

depend. For Concomitant Variations, this further assertion 
has been expressly formulated by Prof. Fowler, as a ' rider ' 
to the canon : — 

If we can assure ourselves that there is no third phenomenon 
varying concurrently with these two, we may affirm that the one 
phenomenon is either a cause or an effect of the other. 

The theory may in fact hold good only np to a certain 
point, — namely, so far as that third phenomenon (which 
let us call Z) is present ; and instead of S — > j&, the law- 
should be accurately expressed S (when Z is present) — > £. 
A well-known example of this is the contraction of water by 
cold, down to 39°, after which it begins to expand again. 
Here the limitation * above 39° ' must be added to the first 
crude statement of the law * water contracts with cold.* 

I may add a further difficulty to which the method of 
concomitant variations is liable : namely, that the supposed 
law guaranteed by it may be a case of vcrrepov Trportpov. 
Finding that the size of towns varies concomitantly with the 
size of the rivers on which they are built, an incautious 
reasoner might conceivably arrive at the law that the size of 
the river was due to the size of the town. Hearing the 
cuckoo call its own name, he might conceivably put this 
down to the cleverness of the bird. Finding Hamlet full of 
' quotations ' he might suppose that Shakespeare was sadly 
wanting in originality. Of course, these extreme cases are 
mainly useful as affording food for the comic papers ; but 
in serious inquiries such as that of the concomitant varia- 
tions between new organic structures and the need for them, 
the fallacy is perhaps not quite unknown. Or again, take 
as an example the good old farmers' theory that ' blight ' was 
either itself a hind of disease, or at least a sign of existing 
disease, in plants. They pictured the plant 'becoming 
diseased/ — much as a man's digestion might get out of 



THE METHODS, IN GENERAL. 351 

order; and, as an effect of this, the "blight was supposed to 
■ come out,' — much as the man might break out in a rash, or 
pimples. But it seems to be now completely established that 
the true explanation is that blight is a kind of fungus, the 
spores of which take root equally in the leaves of healthy 
plants and unhealthy ; but that, however healthy the plant 
may have been, the parasite drains its life, and so causes 
disease, — stunts the growth of the plant, or taxes its fruit- 
bearing powers, or in some way interferes with the normal 
state of things. It is thus often an exceedingly difficult 
matter to say which of two things, varying concomitantly, is 
cause and which is effect ; and the common-sense view, based 
perhaps on some loose analogy, is as likely as not to reverse 
the sequence. 

TJie Methods, in general. 

This, then, is the difficulty attending the application of 
all the methods, — the possible presence, unsuspected, of a 
third phenomenon (or * unknown antecedent ') in the cases 
observed : so that the real law, instead of S — > J», should 
be either Z — > j?, or SZ — > j&. The first of these two 
alternatives (namely that S is purely accidental to je) may 
be for practical purposes excluded by the Doctrine of Chances : 
the second alternative must remain in every case possible, 
until removed by special evidence outside and beyond the 
mere fact of ■ employing the method.' 

To sum up : — Where the Method of Agreement is employed, 
evidence should be further produced, to show (1) either that 
every element but S and je has been eliminated, or (2) that 
those remaining are accidental to £ ; and also that the Plu- 
rality of Causes does not here interfere. 

Where the Joint Method is employed, we require to know 



352 APPENDIX. 

further that no other operative antecedent was present in 
the positive set of cases and absent in the negative ones. 

Where the Method of Difference is employed, we must be 
sure that only one circumstance has been added. 

Where the Method of Eesidues is employed, we require 
the same external evidence as for the Method of Agreement. 

Where the Method of Concomitant Variations is employed, 
we must be further assured, (1) that nothing besides S varies 
concomitantly with Jd ; and (2) that whichever (S or j*>) is 
supposed to be the cause of the other, is not in reality the 
effect. 

In each case the real cogency of the argument depends 
upon the certainty obtainable on these points : obtainable by 
any external (and especially instrumental) correction of our 
observations, and by searching analysis of the phenomena 
observed. The mere statement of the method employed is 
not by itself a sufficient guarantee : at most it may serve to 
point out the special direction in which we should look for 
dangers, and guard against them. 

The two main modes of Inductive fallacy known by the 
time-honoured names of Inductio per enumerationem simpllcem, 
and Post hoc ergo propter hoc, correspond essentially to failures 
in guarding against the dangers of the unaided methods of 
Agreement and Difference respectively. Valid induction 
often enough begins by simplex enumeratio ; and post hoc often 
sets us on the track of a law : indeed it is difficult to suppose 
any other beginnings that can be called beginnings of know- 
ledge. But it is when the attempt is made to rest proof on 
these alone, that the characteristic imperfection of all the 
methods comes to be important. Unaided by special know- 
ledge of the circumstances, they are suggestive guides but 
uncertain tests. 



THE MOODS OF EXCEPTIVE DISPROOF. 353 

C* 

THE MOODS OF EXCEPTIVE DISPROOF. 

Before tracing in detail the reduction of the fourteen 
syllogistic moods in I and to the two formulas given on 
p. 242 above, f there is a less wide and general view that may- 
be taken for a moment with advantage ; and that is, the 
view of them as reducing a generalisation to absurdity by 
means of the modes of positive deductive proof. In every 
valid syllogistic mood there must be at least one positive 
indication among its premisses, and if such premiss be com- 
bined with the contradictory of the thesis (i.e. with the posi- 
tive assertion which such Thesis just denies) we get as a new 
conclusion either the contradictory or the full contrary of the 
other premiss. If, then, both premisses be in fact true, the 
contradictory of the Thesis cannot be true : that is the Thesis 
itself must be so. Thus in the mood Barolco, the Thesis being: 

-\ — > je, its contradictory is S > J© : combine this with 

the positive premiss jfe > M, and (by Barbara) we get the 

conclusion S > M. But this contradicts the remaining pre- 
miss of BaroJw, namely S -\ — > M, and accordingly one of the 
premisses in our Barbara must be materially false. But the 

premiss j& > M is given true : thus the fault is shown to 

lie in the remaining premiss S > j& : and this being false, 

our Thesis is necessarily true. It is needless to set out all the 
forms, but if the reader cares to trace the process in them, he 
will find tfcat Bolcardo also employs Barbara: that Festino 
and Disamis employ Celarent : Ferio employs Cesare : Darii, 
Felapton, and Ferison employ Camestres ; while the four 
moods belonging to the fourth figure employ Camenes. 

* See p. 241. 

f And see formulae (1) and (11) on p. 355. 



354* APPENDIX. 

In practice, however, any method based on this view of 
the argument from exception would, I think, be found 
intricate and unwieldy. The only purpose of mentioning 
it is in order to admit that on occasion the arguments from 
sigu and from essential difference (and even the almost non- 
existent form Gamenes) may be thus utilised in Disproof by 
exception. But since all are also translatable into one 
or other of the two forms above given, which two are in 
a sense typical and fundamental ; and since, in fact, the 
amount of translation necessary in order to bring them 
under the appropriate formula is of the easiest possible 
description, it seems better worth while to follow the 
inquiry in this direction. 

If we take the fourteen syllogistic moods whose conclu- 
sions are in I and 0, it will be seen that these two formulas 
are generalised from them, by omission of the distinctions of 
quality in M and j& respectively, by free employment of the 
law of counter-indication, and by confining attention to 
the smallest amount of assertion necessary. There is only 
one, for example, which exactly corresponds with our first 
formula, namely Baroho, and only one which exactly coi re- 
sponds with our second, namely Bokardo. All the others 
may be viewed as varieties of these two. 

Thus, in the first place, with M negative instead of 
positive, we get Festino ; with M and je both negative and 

with the counter-equivalent of the required non-j& > non-M 

(namely M > j£) we get Darii. With these differences 

and also with the counter-equivalent of the required S -\ — > 
non-M (namely M H — > non-S) we get Datisi ; and if instead 
of merely M H — > non-S in this latter mood we can make 
the positive assertion M — > S, we get Darapti. With M nega- 
tive and with the counter-equivalent of the required Jd > 

non-M (namely M — > non-j&) we get Ferio ; with the same 



THE MOODS OF EXCEPTIVE DISPKOOF. 



355 



differences and also the counter-equivalent of the required 
S 1 > non-M (namely M H — > non-S) we get Ferison ; and 
if here we can make the positive assertion M — > S, we get 
Felapton. Finally, with M negative, and only the minor 
premiss reversed (namely M H — > non-S instead of S H — > 
non-M) we get Fresison ; and if this be strengthened into 
M — > S, we get Fesapo. 

Similarly, in the second class, with j© negative we get 
Disamis ; with the same difference and also with the counter- 
equivalent of the required M -\ — > non-j& (namely Jd H — > 
non-M we get Dimaris ; and if this be strengthened into the 
positive assertion j& — > M, we get Bramantip. 

A table may be of service to the reader in verifying 
these details : — 



(1) Baroko . 




| s+>s 


for S -h> M 


ind $ -> M \ 




(2) 

(3) 


Festino . 




1 Ditto 


„ S+> non-M 


„ S — >• non-M 




Darii 




S -f-^. non-S 


„ S -+-> non-M 


„ M -> S 




(4^) 1 Datisi . 




1 Ditto 


„ M -f-> non-S 


„ M -> S 




(5) Darapti . 




1 Ditto 


„ M— >S 


„ M->S 


First 


(6) 


Ferio 




| so-s 


„ S+> non-M 


„ M — ^ non-5. 


formula. 


(') 


Ferison . 






Ditto 


„ M-|->non-S 


„ M — ^ non-S 




(8) 


Felapton 






Ditto 


„ M— >S 


„ M — ^- non-S 




(9) Fresison 




1 Ditto 


„ M -}-> non-S 


h S — ^ non-M 




(10) 


Fesapo . 




1 Ditto 


„ M— >S 


„ S — ^ non-M 
















(11) 1 Bokardo. 




1 Ditto 


„ M— >S 


„ M +> £ 


) 


(12) 


Disamis . 




1 S •+->• non-S 


„ M— >S 


„ M -f-^ non-S 


l Second 
i formula. 


(13) 
(14) 


Dimaris 






Ditto 


„ M— >S 


„ S -B* non-M 


Bramantip 




1 Ditto 


„ M— >S 


„ S — > M 

" ^ 4 






It will be 


se( 


^ 


that the 


syllogistic moods corresp 


onding 



350 APPENDIX. 

to our first formula are nearly three times as numerous as 
those corresponding to the second ; but the second is not on 
this account at all less important, or even less frequently 
met with in practice. All the syllogistic moods are possible, 
indeed, but some are no more than possible, and certainly 
not all these fourteen forms are equally employed. Probably 
the seven commonest are Baroko, Festino, Darii, Ferison, Datisi, 
Bokardo, and Disamis. Of these the six last form three 
pairs, differing only in the quality of J&; the reason that 
Baroko has no kindred form in I is that for such form the 

disjunctive non-5 > M would have been required, and 

the disjunctive had no place amongst the moods of the 
scholastic scheme. 



D.* 

INVARIABLE SUCCESSION. 

In accordance with the plan proposed in this book, I have 
tried to keep away from all the deeper problems in the 
theory of causation. This was partly on account of their 
difficulty, but also because, whatever other elements may be 
involved in the notion of causal sequence, the element of 
invariability appears strictly sufficient for the purposes here 
aimed at. 

The ' cause ' of a thing comes now more and more 
to mean its 4 history.' The assumptions seem more and more 
justified, that if past events had been at all different this 
present event or thing would not have been precisely what 
it is ; that if they had been ■ essentially ' different this 
would have been essentially different also ; and hence, that 
if the essential part of this event be fixed by definition, to 
* See p. 81. 



INVAEIABLE SUCCESSION. 357 

such essential part there corresponds a part of the antecedent 
history, which not happening the event in question (happen- 
ing there and then) would have been too different to deserve 
its present name. 

But, as noticed elsewhere, the fixing of a definition is 
never " particularisation to the full." Hence, within the 
limits allowed by the name, there is room also for difference 
in the antecedent circumstances (i.e. for Plurality of causes), 
and therefore we are led to read the essentiality only from 
effect to cause (the indication from cause to effect), and to 
use the concept ' invariable law ' in preference to that of the 
* identity ' of cause and effect. 

In all cases of • invariable ' sequence in which S and jg 
are not regarded directly as cause and effect, the assertion of 
invariability is either expressly stated as conditional, or 
intended as tentative (or ' empirical ') only. In the often- 
quoted case of day and night, for example, experience tells 
us not only that day always follows night, but also that night 
follows day, and, further, that day always follows sunrise and 
night sunset. We thus get a double observation (under the 
joint-method) in favour of the commonly received explana- 
tion of the phenomena, while the supposed assertion, ' night. 
causes day,' could only rest upon the method of agreement, 
and, even in the absence of the other explanation, would be 
of very uncertain tenure, — being no explanation of more 
than half the facts observed. It would be an empirical law, 
entirely unconnected either with wider laws which might 
explain it, or with other facts which itself might explain ; 
and it would also be open to the obvious ciiticism that 
nothing had been shown to prove that the dependence was 
not exactly the reverse way, — day causing night, as daily 
exertion (it might be suggested by the poetic mind) causes 
nightly sleep. 



358 APPENDIX. 

Invariability of succession is then what, in assertions of 
causation, we always do mean to express, whether we also 
include Unconditionality (or Efficacy), or keep our assertion 
close to the facts from which these highly abstract notions 
take their rise. The sequence of night and day, viewed 
merely as sequence, and apart from all question of efficacy, 
is not contradicted by the establishment of the surer sequence 
" Earth's revolution in sunlight — > day and night alter- 
nately," but is merely merged in this, and loses thereby 
whatever independent value it might otherwise have had as 
an engine of explanation and prediction. So far as it is for 
these two purposes only that we need, or use, the notion of 
Causation, Invariability is sufficient. 

Nor, on the other hand, if we picture causes as liable to 
' counteraction,' need the absence of actual invariability 
present a stumbling block. Although, for example, the 
majority of seeds never actually come to anything, our 
knowledge of the causes of failure permits us to infer that 
but for certain obstacles that may be classed and numbered, 
they would do so. So far only as the definite possibilities of 
counteraction remain unknown, so far we admit an element 
of uncertainty in any predictions based on our causal law. 
In such a case the statement of the law itself is felt to need 
some further limitation. 




APPENDIX. 



359 



E. 

TABLE I.* 

Abstract and Concrete, Affirmation and Denial. 

[— >• being the symbol of indication ; -f-> for exceptive and simple 
denial of indication ; and , — ' for the assertion of difference.] 

Propositions. 



Unreal. 



Abstract. 



Real. 

I 



Concrete. 



Assertive 
(or affirmative). 

{e.g. 'Children 

never tliink of 

others.') 



Denial. 



Exceptive 

S-|->S. 

{e.g. ' Some 

children are 

unselfish.') 



Assertion of 

difference. 

S,— £. 

{e.g. 'Whales 

are not 

fishes.') 



Assertive 

(or affirmative). 

This S — > «.. 

{i.g. 'This was due 

to carelessness.') 



Denial. 



Simple. 

This S -H> £. 

{e.g. 'This was 

not due to 
carelessness.') 



Assertion of 
difference. 
This S ss Sb. 
{e.g. 'This 
case differs 
from that.') 



See pp. 41-13. 



3G0 



APPENDIX. 



TABLE II.* 

Succession and Co-existence. 
Real Propositions. 

(Whether abstract or concrete, assertive or negative : the symbol -~> 
being used to generalise — ^ and +^>.) 



Of succession. 



Of co-existence. 



Explanatory 
and detective. 



S -J-^ past &. 

Valleys are due to 

denudation.' 
This mark was caused 

by ice.' 



B 



Predictive. 



future &. 



Deficient education 
favours crime.' 

This law will not 
pacify Ireland.' 



Descriptive, 

classifying, 

and connecting. 



S ^-^ present S>. 

S ' — present S>. 

'Gold is an elementary sub- 
stance.' 

•Business qualities and the san- 
guine temperament generally 
go together.' 

* This man is guilty.' 

1 Whales are not fishes.' 

* This case differs from that.' 



[This table intentionally leaves out of consideration the further dis- 
tinctions due to ' laws only roughly true : ' for these, see Table III.] 



• See pp. 79-83. 



APPENDIX. 



361 



TABLE III.* 

The Questions, regarding Indication, to oxe oe which every 
Thesis gives the answer Yes or No. 



)oesS— >S?— 
S being given, 
and £> doubt- 
ful, except 
in the case 
marked *). 



S> in the past re- 
■ latively to S. 



being spoken j j? in the present 
of in the ab- ~~\ — relatively to S. 
stract. 



/The asserted in- \ (Is £> neces- 
dication being (_ sary to S as 
strictly inter- / cause?) 



preted. 

With unex- 
pressed quali- 
fication. 

'Strictly. 



SS in the future 
" relatively to S. 



(Is 5 one cause 
ofS?) 



(Does £> always 
co-exist with 
S?) 



With unex- ^ (Does £? usually 
pressed quali- [■ co-exist with 
lication. ) S :) 

r Strictly. (Is «. the in- 

evitable effect 
of S .') 



. I With 
I pres 
V heat 



S being spoken 
of in the con- ' 
crete (i.e. as 

- particularised 
by its indivi- 
dual peculi- 
arities and 
environment). 



unex- ] (Does S tend to 
pressed quali- V produce <s> ?) 
lication. ) 



* (Was the actual sequence or co-existence, S followed 
or accompanied by £■, other than accidental ?) 

- S ^; , i«.yts e }ovm S fonowS ? ) 



• See pp. 41-83. 



362 



APPENDIX. 



TABLE IV* 

The Types of Akgument. 

Arguments. 



By Example. 



By Sign. 



I 
Analogy. 



(S — Z 

for 
£-Z.) 



Proof of Law 
from Fact. 

(M-^.Z 

for 
here are cases 
of which this 
law is the best 

explanation.) 



Proof 
by Sign. 



(S 



-£ 



► M 



Distinction by 

Point of 

Difference. 

(S~&: 

for 
S-^M 



Exceptive 
Disproof. 



*• 



By Sign or 
non-M.) Difference. 

for 

S-^M.) 



By Example 



* See pp. 224-2S8. 



APPENDIX. 



363 



TABLE V.* 

The Dangees Peculiar to the Special Types or Argument. 

In the Argument : — 



By Example. 

(Danger : unsuspected and essential 
difference.') 



By Sign. 

(Danger : acceptance of a Principle 
which does not apply. 



(1) Analogy. (2) Generalisation. 

(Danger : essen- (Danger : essen- 

tial difference be- tial difference be- 

tween S and «>.) tween This S and 

All S.) 



(3) Ignorance that 
Principle and 
Application are 
needed: or ivhat 
they should be. 



(4) Acceptance of the 
reciprocal of 
either Principle 
or Application as 
equivalent. 



Unsuspected difference 
or resemblance be- 
tween the 'things ' 
spoken of, through 
the influence of 



(6) Difference between 
things named 
alike. 



(6) Resemblance be- 
tween things 
named differ- 
ently. 



* See pp. 252-297. 



INDEX 



Absence, indication by, 84, 92 ; and 
presence, specially defined, 85. 

Abstraction, in general, 72, 333 ; 
abstract propositions, 66, 76, 78, 
80, 112, 235, 272, 276, 339 ; ab- 
stract terms, 72. 

Absurdity, reduction to, 29S, 171, 
251, 286, 307, 326, 328. 

Accident. See Essence. 

Accidentis Fallacia, 293, 176. 

Adequacy of Reason given, 111, 
102, 300, 26. 

Admissions, appeal to, 114, 181 
note, 207. 

Affirmation and Denial, 64, 68, 
223, 243. 

Agreement, Method of, 342, 281, 
339, 351 ; as to meaning, neces- 
sity of, 16, 57, 65, 145, 183. 

Alternative theories, need for con- 
sidering, 39, 40, 164, 177, 270, 
275, 276, 310, 311, 328; list of, 
333. 

Ambiguity, verbal, 124, 133, 177, 
184, 189. 

Analogy, as argument, 226, 252, 
179, 212, 214; and metaphor, 
198 note, 259 ; and essential re- 
semblance, 227, 247, 267; and 
deduction, 229 note, 231, 232, 
234, 254 ; dangers of, 252 ; vital 
point of, 267 ; usual modes of 
employing, 262 ; analogical con- 
sistency, 110, 104. 

17 



Analysis, value of, 258, 237, 273, 
279, 317 ; and synthesis, 259. 

Analytical proposition, 42 note. 

Antecedent and Consequent, 222, 
290. 

Antecedents, unknown, danger of, 
270, 279, 284, 349, 351. 

Application, of Principle, 111, 113, 
103, 109, 204, 208; remote and 
direct, 303, 308, 210. 

Argument, real and verbal, 204 ; 
special types of, 202 ; as com- 
plex proposition, 100, 58, 64, 
310 ; and rules for debate, 160, 
163 ; by example, 224, 220, 252 ; 
by sign, 239, 286, 220; hypo- 
thetical and categorical, 'Sl\ \ 
ad hominem, 61, 181 note, 205; 
by analogy, 226, 252, 179, 212, 
214; inductive, 234, 267; de- 
ductive, 242, 286; chain, 210, 
303, 308; obstruction of, 50, 
128, 167 j a list of objections to, 
178. 

Aristotle, 174, 176, 179, 193, 209, 
293. 

Assertion, in general, 41 ; and 
denial, 64, 68, 223; and con- 
clusion, 33, 18, 41, 150; unsup- 
ported, 147, 326; of difference, 
68, 246; of doubt, 153 ; implied 
by Thesis and Eeason, 99, 26, 
27, 114, 288, 300 ; goal and start- 
ing-point of, 54 ; degrees of 
reality in, 146 ; suggestive and 
tentative, 151, 227, 252, 259, 



866 



INDEX. 



162, 188 ; vagueness of, 49, 187, 
251; and meaning, 26, 60, 63, 

183. See also Proposition. 
Associations, gathered, in names, 

184, 191, 199. 
Assumptions, covert and open, 180, 

181 note, 194, 198 note ; neces- 
sary for language, 13, 46, 106, 
134; for explanation and pre- 
diction, 13, 272, 302. 

Attack, successful resistance to, 
37, 38, 249, 273. 

Axiom, and undeniability, 285 ; 
and theory, 207, 285 ; and plati- 
tude, 80; proof of, 343 note, 
349 ; of Syllogism, 301 ; of 
Causation, 272, 302. 

Axioms, of Consistency, 105, 14, 
21, 46, 122, 208 ; for the indue 
tive methods, 340. 



B. 



Bain, Professor, 56, 87, 89, 105, 
125, 134, 142, 222, 274, 347, 
348. 

Belief, reasons and causes of, 33; 
rationalisation of, 111, 213 ; 
difficulties of grounding, 33, 46, 
48, 149, 309; repression of, by 
Logic, 20, 314, 326 ; in Mystery, 
48, 140, 315; unbelief and dis- 
belief, 153, 326 ; provisional, 94, 
164; and opinion, 162, 151, 98, 
325 ; fluctuation between con- 
tradictory beliefs, 120, 140. 

Bentham, George, 190. 

Bentham, Jeremy, 193. 

Berkeley, 72. 

Bulls, 129. 

Burden of Proof, 148, 217, 277, 
310, 325. 



a 



Casuistry, 132, 253. 
Categorical proposition, 73; argu- 
ment, 221. 



Causation, metaphysics of, 14; 
axiom of, 272, 302 ; propositions 
asserting, 54, 79 ; and indica- 
tion, 79, 82, 268, 356 ; and 
counteraction, 80, 270, 342, 358; 
and uniformity of nature, 272, 
302, 356 ; causal dependence, 
63 ; and efficacy, 358 ; kinds of 
cause, 334, 269 ; identity of 
cause and effect. 357 ; vera causa, 
238, 347, 348 ; plurality of causes, 
80, 270, 342, 351; ancestral 
cause of coexistent events, 336, 
278 note ; cause and history, 
356. 

Chain arguments, 210, 303, 308. 

Chance, teudency, and law, 81, 
268; elimination of, 274, 351, 
270; necessity of recognising, 
337, 81. 

Circle, 120, 169, 213. See also 
Petitio Principii. 

Circular definition, 123, 142. 

Circumstances, essential, 272, 340; 
control of, 281, 346 ; exact simi- 
larity impossible, 272; circum- 
stantial evidence, 221, 224. 

Classification, 63, 64, 171 ; and see 
Names ; of fallacies, 170, 171, 
176 ; classifying propositions, 
53, 54, 79, 83. 

Co-effects, 335. 

Co-existence, 64 ; and succession, 
78, 46, 278 note, 281, 325, 337 ; 
incomplete indication of, 82 ; 
and ancestral cause, 336. 

Coincidence. See Chance. 

Common sense, untrustworthiness 
of, 2, 4, 5, 77, 98, 160, 169, 317, 
321, 323. 

Compartmental view of proposi- 
tions, 53. 

Complex proposition, only gradu- 
ally distinct from simple, 56 ; 
argument as, 58, 64, 100, 310. 

Conclusion, 33, 41 j and thesis, 18, 
150. 

Conclusive proof, 40, 114, 157, 204, 
220, 275, 285, 300, 329. 



INDEX. 



067 



Concomitant Variations, method 
of, 348, 339, 343, 352. 

Concrete. See Abstraction. 

Confusion, fallacies of, 170, 173, 
177. 

Congruent facts, as Proof, 219, 
224, 215, 279. 

Connotation, 53 note, 107. See 
also Meaning. 

Consistency, 103, 109, 114, 207, 
317, 328; Axioms, Maxims, or 
Postulates of, 105, 14, 21, 46, 
122, 208; deductive and analo- 
gical, 110, 103, 104. 

Continuity of Nature, 336, 133, 
14. 

Contradiction, law of, 105, 106, 
109, 328. 

Contradictory instance, 250, 271, 
275, 283. 

Contraposition, 84, 87. 

Conversion, 84, 87. 

Copula, 54. 

Counteraction, of law, 82, 270, 342, 
35S. 

Counter-indication, law of, S4; and 
contraposition, 84 note, 87 ; gives 
the sole equivalent form, 86, 
208; table of, 87; use of, 84, 
89, 310, 329 ; value chiefly nega- 
tive, 90; and the disjunctive 
proposition, 92; applied to con- 
crete propositions, 95 ; as re- 
gards past and future, 96. 

Criticism, value of hostile, 33, 3D, 
60,204,232,301,315. 

Crucial instance, 235 note. 



Deduction, 110 note, 330? and 
Syllogism, 113, 212, 300; and 
Induction, 212, 177, 330, 204; 
and Proof, 213, 217 ; and Pt-titio 
principii, 194; and Analogy, 231, 
229, 234, 254; and Inference, 
216 j principle required for, 213, 



245, 2S7, 288, 290; deductive 
consistency, 110, 108 ; deductive 
argument, kinds of, 242; dangers 
of, 286, 287. 

Definition, consists in exclusion, 
39, 93 ; limits of, 140 ; per genus 
et dijferentiam, 108 ; ordinary, 
best, and special, 125, 127, 137 ; 
as remedy for unreal assertion, 
119, 127, 134; difficulties of, 
124, 127, 133; circular, 123, 
142; ignotum per ignotius, 142; 
definitions as postulates, 122. 

Demonstration, as an ideal, 301, 
195, 232 ; how far conclusive, 
205; and Keal proof, 203; im- 
mediate and mediate, 95, 208 ; 
demonstrative arguments rare, 
209. 

De Morgan, 92. 93, 130, 150, 159, 
180, 193, 194, 251. 

Denial, 64, 68, 223, 243; exceptive, 

68, 219. 
Denotation, 107. 
Dependence, 63, 74. 
Descriptive proposition, 54, 83. 
Dictum de Omni, 301. 
Difference, 108, 135, 255, 281, 294, 

302, 330, 341; power of seeing, 
256, 193, 330; essential, 247, 
248, 356; indistinct, 246; as- 
sertion of, 68, 246 ; points of, 

69, 228, 246; neglect of, 108, 
254, 256, 270, 293 ; method of, 
345, 277, 281, 339, 352 ; distinc- 
tion by point of, 246, 241. 

Dilution of Fallacy, 130, 196. 

Disbelief and unbelief, 326, 154. 

Discovery. See Inference. 

Disjunctive proposition, special 
danger of, 92. 

Disproof, and absence of proof, 
151, 165 ; as means to proof, 
113; exceptive, 249, 353, 241, 
242; frustration of, 149, 310; 
use of syllogistic moods in, 243, 
248 ; easier than proof, 250, 275, 
279 ; under Method of Residues, 
348. 



INDEX. 



Distinction by point of difference, 

246, 241. 
Division, line of, 133, 39, 93, 106, 

124. 
Doubt, assertion of, 153. 



E. 



Efficacy in causation, 358. 

Elements of an event, 237, 272, 
340, 348. See also Analysis. 

Elimination of Accident, 274, 351, 
270, 340. 

Ellipsis in expression, 189, 210, 
- 260. 

Empirical law, 285, 286, 357; 
proof, 234, 19, 204, 212, 215, 
217; methods, 277, 339. 

Enumeratio simplex, 270, 352. 

Epigram, 45, 129, 132. 

Error, reduction to minimum, 117; 
psychology of, 14, 22. 

Essence, and accident, 83, 293, 
335, 336 note, 338; essential 
resemblance, 229^ 64, 253, 254 ; 
ditto asserted in every analogical 
argument, 266 ; essential dif- 
ference, 247, 248, 356; essential 
elements of an event, 237, 272, 
340, 348 ; essential and acci- 
dental propositions, 42, 125. 

Establishment by testing, 37, 39, 
249. 

Etymolosrv, use and abuse of, 37, 
105, 190. 

Events, as abstractions, 333 ; ana- 
lysis of, 237, 272, 340, 348. 

Evidence, 21, 148; varies in 
strength, 40, 308, 311, 328; 
relevancy of, 101, 111, 182 ; 
hearsav, 148. 221 ; circumstan- 
tial, 221, 224; aid of special 
knowledge in judging, 22, 25, 
26, 310. 

Example, argument by, 224, 220, 
252. 

Exception, and rule, 36, 249, 273, 
271, 279. 



Exceptive denial, 68 ; disproof, 
249, 353, 241, 242. 

Excluded Middle, law of, 1S5, 105, 
106. 

Exclusion and definition, 39, 93. 

Experimental (inductive, or empi- 
rical) Methods, general discus- 
sion of, 277; in detail, 339; as 
means of discovering exceptions, 
274; as shifting burden of proof, 
277; as ideals, 282, 310; re- 
ducible to two, 281, 339; un- 
satisfactoriness of, 282, 339 ; 
fundamental resemblance of all, 
282 ; further evidence required 
in, 279, 351 ; experiment, pre- 
cautions in, 277, 309, 352. 

Explanation, the counterpart of 
Proof, 111; assumptions required 
for, 13, 272, 302 ; and reduction 
to law, 74 ; limits of, 128, 142 ; 
the 'best,' 250, 271, 272; ex- 
planatory propositions, 83, 123, 
219. 



F. 



Fact, and law, 66, 61, 22 i, 219, 
215 ; and theory, 161, 207 225, 
279, 76, 157, 213, 306; con- 
gruent, 219, 224, 215, 279. 

Factor overlooked, 201, 181, 252, 
278. 

Fair presumptions, 158, 94. 

Faith and hesitation, 162, 285, 
314, 331. 

Fallacy, and Sophism, 9; study of, 
8, 22; real and verbal, 214, 204; 
avoidance, detection, and con- 
viction of, 22, 23, 31, 118, 200, 
287, 291, 298; classification of, 
170, 171, 176; dilution of, 130, 
196 ; various senses of, 172 ; 
mav be due to several causes, 
170, 289. 

Fluctuation of belief, 120, 140. 

Formal adequacy of Reason, 26, 
111, 102, 300. 



INDEX. 



3G9 



Fowler, Professor, 237, 340, 341, 
343, 344, 347, 350. 

Further assertion implied by The- 
sis and Reason, 26, 27, 99, 114, 
288, 300. 



G. 



Gaps in reasoning, 114, 210, 310, 

311, 326. 
Generalisation, and abstraction, 

72, 333; attack on, 279; rests 
on neglect of difference, 251, 
272; and exception, 273, 279; 
implied in concrete proposition, 
76; danger of, 270, 256. See 
also Law. 

General Names, use of, 107, 190; 

and symbols, 96; and definition, 

124, 133, 141. 
Genus, and Differentia, 108, 135, 

255, 281, 294, 302, 329, 344; 

summum, 141. 
Grammar, and Logic, 15, 57, 65, 

73, 183,221, 223; and Language, 
4, 64, 66, 69, 73, 97, 183. 

Goal of an assertion, 54. 
Guesswork, employment of, in de- 
tecting Fallacy, 169, 218. 
Guidance of reasoning, 17. 



H. 

Hamilton, Sir W., 18, 42. 

Hearsay evidence, 148, 221. 

Hesitation, 162, 285, 258, 314, 331. 

Hypothesis, 164, 215, 271, 283, 
285 ; hypothetical proposition, 
67, 73 ; hypothetical argument, 
221. 



I. 



Identity, law of, 105, 106, 109, 
122 ; of cause and effect, 357 ; 
identical propositions, 42. 

Ignorance, profession of, 154, 156. 



Ignoratio elenchi, 182, 121, 150 
note, 177, 178, 197 ; finer shades 
of, 189. 

Ignotum per ignotius, 142. 

Illicit process, 173, 223. 

Illusion, 181, 207, 322. 

Immediacy of sequence, 2S1. 

Immediate inference, 95, 208. 

Implication, and Logic, 21, 25, 
107; and Indication, 60. See 
also Meaning, and Consistency. 

Import of propositions, four views 
of, 53. 

Impossibile, ductio per, 174 note, 
353. 

Inconceivability of opposite, 285. 

Inconsistency. See Self -contradic- 
tion. 

Indication, the most general rela- 
tion, 59; and sign, 79, 107, 113, 
239, 245, 301 ; and names, 107 ; 
contrasted with implication, 60; 
chief difficulty of the name, 61; 
abstract and concrete, 61, 62; 
incomplete, 80, 268 ; law of 
counter, 84; in concrete propo- 
sition, 61; in induction, 214, 
309 ; time-element in, 96 ; of 
Thesis by Reason, 99, 204, 211, 
244, 310, 329; and causation, 
79, 82, 268, 356; and meaning, 
60, 63, 107. 

Indistinct difference, 246; resem- 
blance, 226. 

Individuality, and differentia, 254. 

Induction, and Logic, 276, 330 ; 
and neglect of difference, 2/0; 
contrasted with deduction, 212, 
177, 204, 330; dangers of; 267, 
270 ; and incompleteness of 
Principle, 214, 308, 309 ; induc- 
tive inference and proof, 215, 
234, 272; inductive methods, 
277, 339; and unknown antece- 
dents, 270, 279, 284, 349, 351. 

Inference, ambiguities of the name, 
32, 34; and Proof, 17, 31, 68 
note, 94, 97, 214, 217, 227, 347, 
352; immediate, 95, 208; de- 



370 



INDEX. 



pendence on deduction, 216 ; 
fallacies of, 1 77. 

Inquiry, stifling of, 154. 

Instance, contradictory, 250, 69, 
271, 275, 283; crucial, 235 note. 

Intention of speaker, 16, 65, 69, 
70. 

Interpretation, and Logic, 16, 21, 
183; and counter-indication, 89; 
of Principle, 103, 109. See also 
Meaning and Misinterpretation. 

Interval between self-contradic- 
tory assertions, 130. 

Invariable succession, 356, 80. 

Irrelevant Reason. Bee Ignoratio 
elenchi. 



J. 



Jevons, Professor, 91, 92, 183, 277, 
309, 349. 

Joint method of Agreement and 
Difference, 344, 357. 

Judgment, and Thesis, 41, 97 ; 
degrees of completeness in, 41, 
97, 325; presumption involved 
in, 162; reservation of, 150. 
Sea also Belief, and Proposition. 



K. 



Keynes, 96. 

Knowledge, growth of, 75, 212, 
258; need for special, in judg- 
ing evidence, 22, 25, 26, 310; 
generality of, 76. See also Be- 
lief, and Proof. 



L. 



Language, and Grammar, 4, 64, 66, 
69, 73, 97, 183; Logic limited 
by, 45, 47, 132, 187, 321; 
assumptions required for, 13, 
46, 106, 134 ; difficulties of, 133, 
136, 189, 259, 264 j snares of, 



174, 176, 186; and hidden differ- 
ence, 258. 
Law, in Nature, 14, 71, 81, 285, 2/2, 
302 ; and Fact, 66, 61, 224, 219, 
215; and explanation, 74; and 
counteraction, 82, 270, 342, 358; 
and contradictory instance, 249, 
275, 283, 69, 271; empirical, 
285, 286, 357 : chance and ten- 
dency, 81, 268 ; reference to in 
concrete propositions, 76 ; re- 
quired for all rationalisation, 

111, 213, 255. See also Principle, 
Generalisation, Abstract pro- 
position. 

Laws of Thought. See Axioms of 
Consistency. 

Line of division, 133, 39, 93, 108, 
124. 

Logic, and Philosophy, 2, 3, 12, 46, 
142, 313, 323; and Common 
Sense, 2, 4, 5, 77, 98, 160, 169, 
317, 321, 323; and Physical 
Science, 2, 3 ; and Grammar, 15, 
57, 65, 73, 183, 221, 223; and 
Ehetoric, 15, 8, 23, 180, 200, 
259, 263; and Psychology, 14, 
22, 41, 97, 120 ; and Scepticism, 
20, 284, 314, 326, 128 ; and im- 
plication, 21, 25, 107 ; practical 
purpose of, 2, 3, 6, 8, 10, 13, 17, 

112, 117, 276, 326, 331 ; disputed 
points of, 7, 8, 11 ; clumsiness 
of, 9, 320; negative character 
of, 19, 327; pons asinorum of, 
84, 303 ; province of, 12 ; limita- 
tions of, 10, 13, 25, 26, 38, 102, 
117 ; objections to, 7, 314; in- 
ductive and deductive, 19, 110 
note, 212, 276, 330; logical 
dependence, 63 ; logical out- 
come, 103; logical necessity, 207. 



M. 

MacColl, H., 60, 84, 101. 
Margin, doubtful, in names, 134. 
Material obverse, 89. 



INDEX. 



371 



Maxims of Consistency. See 
Axioms. 

Meaning, laws of interpretation, 
21 ; agreement postulated as 
starting-point, 16, 57, 65 ; and 
indication, 60, 63, 107; and 
gathered associations, 184, 191, 
199 ; and definition, 39, 107, 141, 
] 85 note ,• best, nsual, and 
special, of a name, 125, 127, 
137; part forgotten, 126, 292; 
gradual change in, 184, 189 ; re- 
lative to standard, 191 ; of Thesis 
contained in Season, 26, 201; 
meaningless term, fallacy of, 47, 
138; meaningless questions, 45, 
46, 47, 131, 185 note. 

Mediate inference, 95, 208. 

Metaphor, as argument, 179, 259, 
265 ; in names, 189 ; change of, 
261 ; difference from, analogy, 
198 note, 259 ; inclination to- 
wards, 257, 259, 265. 

Metaphysics. See Philosophy. 

Middle term, 222, 229, 234, 239, 
244, 290, 304, 305 ; as sign, 234, 
239; undistributed, 173, 222. 

Mill, J. S., 15, 19, 53, 107, 170, 
172, 174, 177, 230, 274, 277, 310, 
339, 341, 312, 341, 345, 347, 348. 

Miracles, 157. 

Misinterpretation, 182, 169, 173; 
by opponent, 188; and law of 
Excluded Middle, 185; of 
motives, 171, 175 ; accusation 
of, 183 ; avoidance of, 186. See 
also Meaning, and Interpreta- 
tion. 

Modi ponens, tollens, etc., 240, 241. 

Moods of Syllogism, 223, 240, 355. 

Mystery, belief in, 48, 100, 315. 

N. 

Names, twofold use of, 107 ; as 
labels, 109, 245; loose applica- 
tion of, 83, 124, 133, 184, 189; 
question.begging, 198, 264; 



negative, 65, 71, 93 note ; 
gathered associations of, 184, 
191, 199 ; ancestors' mistakes in 
applying, 187. See also Mean- 
ing and Metaphor. 

Nameable things, 13, 53. 

Nature, continuity of , 133, 336, 14; 
explanation of, 302, 272, 13; 
natural laws, 14, 61, 71, 81, 285, 
272, 302. 

Necessary truth, 207. 

Needs of Practice, 4, 13, 20, 38, 
154, 162, 169, 331, 336. 

Negation, in propositions, 64, 68, 
223, 243 j in names, 65, 71, 93 
note. 

Negative, proof of, 250, 346. 

Newman, Cardinal, 66, 296. 

Non Sequitur, 168, 179. 

Nota Nolo?, 245, 301. 

Number of confirmatory facts, 279, 
281, 343. 



Objections, to an assertion, 21; to 
an argument, 178 ; to Logic, 7, 
314. 

Observation. See Experimental 
Methods. 

Obstruction, of argument, 50, 128, 
167. 

Obverse, material, 89. 

Opinion, prevailing, 159; and be- 
lief, 162, 151, 98, 325. 

Opponent, misinterpretation by, 
188. 

Opposite, inconceivability of, 285. 

Over-generalisation, 177, 256, 270, 
293. 



Paradox, 45, 130. 

Parallel cases, 104, 110, 219, 226, 

233. 
Paralogism, 173. 
Particular propositions, 63. 



372 



INDEX. 



Petitio Principii 193, 177, 181 
note, 195, 198, 206, 260, 264; 
and deduction, 194; and tauto- 
logy, 120 ; in names, 198, 264. 

Philology, and unsuspected differ- 
ence, 258. 

Philosophy, and Logic, 46, 2, 3, 12, 
14, 142, 213, 323, 

Platitude, 120, 198. 

Plurality of causes, 80, 270, 342, 
351. 

Point at issue. See Ignoratio Elenchi. 

Points, of difference, 69, 228, 246 ; 
distinction by, 246, 241 ; of re- 
semblance, 228, 253, 300. 

Pons asinorum of Logic, 84, 303. 

Positive assertion. See Affirmation. 

Post hoc, fallacy, 270, 346, 352. 

Postulates. See Assumptions. 

Practical certainty, 38, 94, 205, 
308. 

Practice, needs of, 4, 13, 20, 38, 
154, 162, 169, 331, 336. 

Precautions, in experiment, 277, 
309, 352. 

Predicate, 54. 

Predication-view of propositions, 
53, 54, 231. 

Prediction, and explanation, 13, 74, 
219, 272, 302; predictive pro- 
positions, 83. 

Premisses, 32, 100; major and 
minor, 113, 173, 300. 

Presence and absence, specially 
denned, 85. 

Presumption, fair, 158, 94; in- 
volved in all judgment, 162 ; of 
weakness, 165; raising of, 209, 
263. 

Prevailing opinion, 159. 

Principle, as required for Proof, 
111, 113, 204, 208, 213, 287, 309, 
329 ; interpretation of, 103, 109 ; 
formation of, 104; extent of, 
304, 309, 329 ; in inductive proof, 
213, 214, 226, 267, 309; in 
deductive proof, 213, 245, 287, 
288 290 

Probability, 274, 133, 351. 



Proof, in general, 99, 97, 111, 113, 

214, 329 ; meaning and aims of, 
31 ; etymological meaning of, 
36 ; subject-matter of, 41 ; and 
testing, 35; and explanation, 
111 ; and resistance to attack, 
37; and inference, 17, 31, 68 
note, 97, 214, 217, 347, 352 ; and 
disproof, 113, 151, 165, 250, 275, 
279; and principle, 111, 113, 
204, 208, 213, 287, 309, 329; 
degrees of, 40, 308, 311, 328; 
unavoidable incompleteness of, 
38, 40; need for, 143, 42, 149, 
165; demand for, 165; conclu- 
sive, 220, 40, 114, 207, 275, 285, 
300, 328; empirical and deduc- 
tive, 111, 113, 204, 212, 213, 214, 

215, 217, 272, 300; circum- 
stantial, 221, 224; by sign, 244; 
real, and demonstration, 203; of 
axioms, 343 note, 349; of nega- 
tive, 250, 346; concerned with 
complete assertion only, 41 ; ex- 
cuses for absence of, 166 ; often 
not demanded, 50, 165. 

Propositions, Subject, Predicate, 
and Copula of, 51 ; four views of 
the import of, 53 ; best excuse 
for predication-view, 54 ; start- 
ing-point and goal of, 54, 55 ; 
real and unreal, 41 ; unreal and 
verbal, 42 ; apparently unreal, 
48; tautologous, essential or 
identical, 43 ; synthetical and 
analytical, 42 note ; self-contra- 
dictory, 44; simple and complex, 
56 ; argument as complex pro- 
position, 100, 58, 64,310; affirma- 
tive and negative, 64; abstract 
and concrete, 66 ; abstract-con- 
crete, 77, 276; notional and 
real, 66 note ; exceptive denial, 
and assertion of difference, 68 ; 
particular, 68; categorical and 
hypothetical, 73, 67 ; of succes- 
sion, 79 ; naming, classifying, or 
descriptive, 54, 79, 83 ; explana- 
tory, 83, 123, 219; predictive, 



INDEX. 



373 



83; reciprocal, 89, SS; disjunc- 
tive, 92. 

Proverbs, employment of, 266. 

Province of Logic, 12. 

Provisional beliefs, 94, 164, 316. 

Psvchologv, and Logic, 14, 22. 41, 
97, 120. 



Q. 



See Petitio 



Question-begging. 

princijjii. 
Questions, meaningless. 45. 46, 47. 
131, 1S5 note ; verbal, 144. 



B. 



Eationalisation, of thesis, 111. 213, 
255, 2ss. 307. 

Eead, Carveth r 53, SO, 312. 

Beality, in propositions, 41, 42, 
204, 211 ; degrees of, 146. 

Eeason given, and Thesis, relation 
between, 99, 26, 204, 211. 214. 
288, 300, 310, 329; material 
truth of, 25, 26, 101, 195 ; formal 
adequacy of, 26, 102, 111, 300 ; 
real and verbal, 204; reasons 
and causes of belief, 33. 

Eeasoning, and rationalisation, 
111. 213, 255, 2SS, 307; guidance 
of, 17 ; direct and reflective, 18, 
31 ; chain of, 210 ; gaps in, 114, 
210, 310, 311, 326. 

Reciprocal proposition, 89 and 
note, SS ; acceptance as equiva- 
lent, 91, 173, 2SS, 290. 

Reductio ad absurdum, 298, 174, 
251, 286, 307, 326, 32s. 

Eeflective reasoning, 18, 31. 

Eelation-view of propositions, 53. 

Eelevancy of Eeason, 101, 111, 182, 
191. See also IgnoraHo Elenchi. 

Eelevant fact overlooked, 181, 252. 
278. 

Eesemblance. striking, 227, 256, 
261; essential, 229,64, 253, 251, 



20*: ; neglect of, 108, 257, 293 ; 

indistinct, 226; points of. 22S. 

253, 300; degrees of, 227; of 

circumstances, 272. 
Eeservation of judgment, 150. 
Eesidues, Method of, 347, 339, 352 ; 

disproof by, 348. 
Besistance to attack, 37, 38. 249, 

273. 
Bhetoric, 15, 8, 23, 180. 200, 259, 

263. 
Eival theories. See Alternative. 
Eobertson, Professor Croom, 84 

note. 



s. 



Scepticism, 20, 12s. 2S5. 314, 315, 
326; as an artifice, 153, 326. 

Science, phvsical, and Logic, 2. 3. 

Self-contradiction, 103, 129, 44, 
317, 328; contrasted with tau- 
tology, 129, 130 ; and epigram, 
12'.', 45, 132; requires dilution, 
to be dangerous, 130; interval 
between contradictory asser- 
tions, 131 ; in form of question, 
131; opposite causes of , 132 ; and 
difficulties of language (a 
133 ; verbal, not real, 139, 140. 

Self-deception. 284, 319. 

Self-evident truths, 46, 141 
285. 

Senses, deception of, 2"7. 

Sequence. See Dependence, Suc- 
cession, ayid Causation. 

Sign, and indication, 62, 74, 79, 
90, lu7, 113, 239. 245, 301; and 
symptom, 63. 79, 270, 308; and 
naming, 109 ; and middle term, 
234. 239; by presence and 
absence, 86; a special sense of 
the name, 79 ; argument by, 23'J, 
220. 2s6 ; proof by, 244, 240. 

Similarity. See Eesemblance. 
lea enumeratio, 270, 352. 

Simpliciter et secundum quid, 293, 
294. 



374 



INDEX. 



Sole cause, 269, 334. 

Sorites, fallacy, 133. 

Special circumstances, influence 
of, 67, 68, 72, 282. 

Special knowledge, required in 
judging evidence, 22, 25, 26, 310. 

Species, 255. 

Spencer, H., 20, 47, 53, 130, 190. 
156. 

Starting-point of an assertion, 54. 

Stephen, Sir Jas., 150, 159. 

Subject, of a proposition, pro- 
visionally defined, 42; and 
" things," 51 ; two in a proposi- 
tion, 52. 

Substitution of Similars, 349 note. 

Succession, and co-existence, 78, 
96, 278 note, 281, 325, 337 ; in- 
variable, 356, 80; immediacy of, 
281 ; incomplete indication of, 
79. 

Suggestive assertion, 162, 18S, 151, 
227, 259, 252, 325. 

Sully, J., 14, 181. 

Summum genus, 141. 

Superficiality of view, 201. 

Syllogism, uses of, 114, 181 note, 
289, 300, 304 ; Axiom of, 301 ; 
moods of, 223, 240, 355; and 
proof, 111, 113, 212, 204, 207, 
254, 300 ; syllogistic fallacy, 209, 
288, 289. 

Symbols, danger of, 91, 96 ; need 
of, 322, 327; explanation of 
those here employed: — S, 51"; 
J, 51; &, 54; ->, 62; +>, 68 j 
~, 68; T andK, 99. 

Synthesis, 259; synthetical pro- 
position, 42 note. 



T. 



Tautology, 120, 43, 204 ; causes of, 
121 ; resemblance to Petitio 
principii, 120; chief forms of, 
123 ; hai'mless when used as 
Postulate, 122 ; finer shades of, 
124; Bain's view of verbal pre- 



dication, 125 ; dependence on ex- 
tent of remembrance of mean- 
ing, 126, 292 ; remedy for, 127 ; 
contrast with self-contradiction, 
129, 130. 

Tendency, 81, 268. 

Tentative assertion. See Sugges- 
tive. 

Terms, 51, and see Names ; mean- 
ingless, 138, 47; abstract and 
concrete, 72. 

Test. See Proof and Exception. 

Testimony, 221, 225. 

Theory, 219, 252, 271; and fact, 
76, 157, 161, 213, 326, 207, 225, 
279 ; and axiom, 207, 285 ; alter- 
native theories, 39, 40, 164, 177, 
239, 270, 275, 276, 310, 311, 328, 
333. 

Thesis, defined, 18, 41 ; and con- 
clusion, 18, 150 ; and suggestion, 
122, 325 ; and judgment, 41, 97 ; 
and Reason combined, 26, 27, 
99, 114, 288, 300; indicated by 
Reason, 99, 204, 211, 244, 310, 
329. 

« Things,' 13, 51, 52. 

Truth, accepted, 26, 102, 205; 
necessary, 207 ; self-evident, 46, 
149, 207, 285; material, of 
Reason, 25, 26, 101, 195. 

Tyndall, Professor, 158. 

Types of argument, 202. 



U. 



Ultimate questions, our neglect of, 
46, 3, 12, 142, 171. 

Unbelief and disbelief, 326, 154. 

Unconditionality, 358. 

Undistributed Middle, 173, 222. 

Uniformity, 14 ; and see Law. 

Universe of discourse, 93 note. 

Universal. See Abstract proposi- 
tion. 

Unknown Antecedents, danger of, 
in induction, 270, 279, 284, 349. 
351. 



INDEX. 



375 



Unreal propositions, defined, 42; 

remedy for, 119, 127, 134; 

degrees of unreality, 146. 
Unsupported assertion, 147, 326. 
Untruth implied, 178, 179, 300. 



V. 

Vagueness of assertion, 49, 187, 

251. 
Variations, Concomitant, Method 

of, 348, 339, 343, 352. 
Venn, J., 53, 68, 158, 274, 312. 



Vera Causa, 238, 347, 348. 

Verbal propositions, 42, 125; 
verbal ambiguity, 124, 133, 177, 
184, 189 ; verbal questions, 144. 

Verifiability and reality, 147. 



W. 

Whately, Archbishop, 18, 31, 144, 
150, 154, 160, 170, 174, 195, 196, 
263. 

Wundt, Professor, 60, 63, 90. 



THE END. 



Scientific Publications. 



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of Toulouse ; Correspondent of the Institute. With 148 Illustrations. 12mo. 
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"The discussion of man's origin and early history, hy Professor De Quatrefages, 
formed one of the most useful volumes in the ' International Scientific Series,' and 
the same collection is now further enriched by a popular treatise on paleontology, by 
M. N. Joly, Professor in the University of Toulouse. The title of the book, -Man 
before Metals, 1 indicates the limitations of the writer's theme. His object is to bring 
together the numerous proofs, collected by modern research, of the great age of the 
human race, and to show us what man was. in respect of customs, industries, and 
moral or religious ideas, before the use of metals was known to him.' - — New York 
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"An interesting, not to say fascinating volume."— New York Churchman. 

ANIMAL INTELLIGENCE. By George J. Romanes, F. E. S., Zoological 
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" My object in the work as a whole is twofold : First, I have thought it desirable 
that there should be something resembling a text-book of the facts of Comparative 
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they have occasion to acquaint themselves with the particular level of intelligence 
to which this or that species of animal attains. My second and much more impor- 
tant object is that of considering the facts of animal intelligence in their relation to the 
theory of descent."— From the Preface. 

" Unless we are greatly mistaken, Mr. Romanes's work will take its place as one 
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modest preface. The resnlt is the appearance of a collection of facts which will be a 
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present systematically well-assured observations on the mental life of animals."— Sat- 
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"The author believes himself, not without ample cause, to have completely bridged 
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THE SCIENCE OF POLITICS. By Sheldon Amos, M. A., author of " The 
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ANTS, BEES, AND WASPS. A Record of Observations on the Habits of the 
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"This volume contains the record of various experiments made with ants, bees, and 
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" We have no hesitation in saying that the author has presented us with the most 
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DISEASES OF MEMORY : An Essay in the Positive Psychology. By Til 
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MYTH AND SCIENCE. By Tito Vignoli. 12mo, cloth, price, $1.50. 

" His book is ingenious ; ... his theory of how science gradually differen- 
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"An attempt made, with much ability and no small measure of success, to trace the 
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"It is a curious if not startling contribution both to psychology and to the early 
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THE BRAIN AND ITS FUNCTIONS. By J. Lure, Physician to the 
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"No living physiologist is better entitled to speak with authority upon the 
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THE CONCEPTS AND THEORIES OF MODERN PHYSICS. Ey 

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THE FORMATION OF VEGETABLE MOULD, THROUGH TnE 
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mould which covers the whole surface of the land in every moderately humid 
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interest and instruction, as the structure and the labors of the earth-worm.' 1 — 
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" Respecting worms as among the most useful portions of animate nature, 
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SUICIDE : An Essay in Comparative Moral Statistics. By Heney Moeselli, Pro- 
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VOLCANOES : What they Are and what they Teach. By J. W. Judd, 

Professor of Geology in the Eoyal School of Mines (London). With Ninety-six 
Illustrations. 12mo. Cloth, $2.00. 

" In no field has modern research been more fruitful than in that of which Professor 
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book is very far from being a mere dry description of volcanoes and their eruptions ; it 
is rather a presentation of the terrestrial facts and laws with which volcanic phenomena 
are associated."— Popular Science Monthly. 

" The volume before \is is one of the pleasantest science manuals we have read for 
some time." — Athenaeum. 

" Mr. Judd's summary is so full and so concise that it is almost impossible to give 
a fair idea in a short review." — Pall Mall Gazette. 

THE SUN. By C. A. Young. Ph. D., LL. D., Professor of Astronomy in the College 
of New Jersey. With numerous Illustrations. 12mo. Cloth, $2.00. 

" Professor Young is an authority on ' The Sun, 1 and writes from intimate knowl- 
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and opportunities to watch it, and has contributed important discoveries that have 
extended our knowledge of it. 

" It would take a cyclopaedia to represent all that has been done toward clearing up 
the solar mysteries. Professor Young has summarized the information, and presented 
it in a form* completely available for general readers. There is no rhetoric in his book; 
he trusts the grandeur of his theme to kindle interest and impress the feelings. His 
statements are plain, direct, clear, and condensed, though ample enough for his purpose, 
and the substance of what is generally wanted will be found accurately given in his 
pages."— Popular Science Monthly. 

ILLUSIONS : A Psychological Study. By James Sully, author of " Sensa- 
tion and Intuition," etc. 12mo. Cloth, $1.50. 

This volume takes a wide survey of the field of error, embracing in its view not only 
the illusions commonly regarded as of the nature of mental aberrations or hallucina- 
tions, but also other illusions arising from fchat capacity for error which belongs essen- 
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tific* treatment— that is to say, the description and classification of acknowledged errors, 
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" This is not a technical work, but one of wide popular interest, in the principles and 
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of dreams are first considered, and then the author passes to the illusions of introspec- 
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GENEEAL PHYSIOLOGY OF MUSCLES AND NERVES. By Dr. I 

Rosenthal, Professor of Physiology at the University of Erlangen. With 
seventy-five WoodcutB. (" International Scientific Series.") 12mo, cloth, 
$1.50. 

"The attempt at a connected account of the general physiology of muscles 
{and nerves is, as far as I know, the first of its kind. The general data for this 
branch of science have been gained ouly within the past thirty years. 11 — Extract 
from Preface. 

SIGHT : An Exposition of the Principles of Monocular and Binocular Vision 
By Joseph Le Comte, LL. D., author of "Elements of Geology "; "Re- 
ligion and Science " ; and Professor of Geology and Natural History in the 
University of California. With numerous Illustrations. 12mo, cloth, $1.50. 

*■ It is pleasant to find an American book which can rank with the very best 
of foreign works on this subject. Professor Le Conte has long been known as 
an original investigator in this department ; all that he gives us is treated with 
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ANIMAL LIFE, as affected by the Natural Conditious of Existence. By 
Karl Semper, Professor of the University of Wiirzburg. With 2 Maps 
and 106 Woodcuts, and Index. 12mo, cloth, $2.00. 

"This is in many respects one of the most interesting contributions to 
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THE ATOMIC THEORY. By Ad. Wttrtz. Membre de Tlnstitut ; Doyen 
Honoraire de la Faculte de Medecine ; Professeur a la Faculte des Sciences 
de Paris. Translated by E. Cleminshaw, M. A., F.C.S., F. I. C, Assist 
ant Master at Sherborne School. 12mo, cloth, $1.50. 

" There was need for a book like this, which discusses the atomic theory both 
in its historic evolution and in its present form. And perhaps no man of this 
age could have been selected so able to perform the task in a masterly way as 
the illustrious French chemist, Adolph Wurtz. It is impossible to convey to the 
reader, in a notice like this, any adequate idea of the scope, lucid instructiveness, 
and scientific interest of Professor Wurtz's book. The modern problems of 
chemistry, which are commonly so obscure from imperfect exposition, are here 
made wonderfully clear and attractive. 11 — The Popular Science Monthly. 

THE CRAYFISH. An Introduction to the Study of Zoology. By Professor 
T. H. Huxley, F. R. S. With 82 Illustrations. 12mo, cloth, $1.75. 

" Whoever will follow these pages, crayfish in hand, and will try to verify for 
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with all the srreat zoological questions which excite so lively an interest at the 
present day. 11 

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THE HUMAN SPECIES. By A. De Qtjatrefages, Professor of Anthro- 
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The work treats of the unity, origin, antiquity, and original localization of 
the human species, peopling of the globe, acclimatization, primitive man, forma- 
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STUDENTS' TEXT-BOOK OF COEOR ; or, MODERN CHROMAT- 
ICS. With Applications to Art and Industry. With 130 Original Illus- 
trations, and Frontispiece in Colors. By Ogden N, Rood, Professor of 
Physics in Columbia College. 12mo, cloth, $2.00. 

"In this interesting book Professor Rood, who, as a distinguished Professor 
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EDUCATION AS A SCIENCE. By Alexander Bain, LL. D. 12mo, cloth, 
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land."— New York Sun. 

A HISTORY OF THE GROWTH OF THE STEAM-ENGINE. By 

Robert H. Thurston, A.M., C.E., Professor of Mechanical Engineering 
in the Stevens Institute of Technology, Hoboken, N. J., etc. With 163 
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contended, the steam-engine is the most important physical agent in civilizing 
the world, its history is a desideratum, and the readers of the present work will 
agree that it could have a no more amusing and intelligent historian than our 
author."— .Sosfoft Gazette. 

STUDIES IN SPECTRUM ANALYSIS. By J. Norman Lockyer, F. R. S., 
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TEXT-BOOK OF SYSTEMATIC MINERALOGY. By Henry Bauer 
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ANTHROPOLOGY: An Introduction to the Study of Man and Civilization. 
By Edward B. Tylor, D.C. t ,., F. R. S., author of "Primitive Culture," 
"The Early History of Mai^ind," etc. With 78 Illustrations. 12mo. 
With Index. Cloth, $2.00. 

"Mr. Tylor's admirahle little hook certainly deserves the success with which 
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SCIENTIFIC CULTURE, AND OTHER ESSAYS. By Joseph Parsons 
Cooke, Professor of Chemistry and Mineralogy in Harvard College. One 
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POPULAR LECTURES ON SCIENTIFIC SUBJECTS. By H. Helm- 

holtz, Professor of Physics at the University of Berlin. Second Series. 
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The favor with which the first series of Professor Helmholtz's lectures was 
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volume. 

THE POWER OF MOVEMENT IN PLANTS. By Charles Darwin, 
LL. D., F. R. S., assisted by Francis Darwin'. With Illustrations. 12mo, 
cloth, $2.00. 

"Mr. Darwin's latest study of plant-life shows no abatement of his power of 
work or his habits of fresh and original observation. We have learned to expect 
from him at intervals, never much prolonged, the results of special research in 
some by-path or other subordinated to the main course of the biological system 
associated with his name; and it has been an unfailing source of interest to see 
the central ideas of the evolution and the continuity of life developed in detail 
through a series of special treatises, each wellnigh "exhaustive of the materials 
available for its subject."— Saturday Review. 

A PHYSICAL TREATISE ON ELECTRICITY AND MAGNETISM. 

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With about 200 full-page and other Hlustrations. 2 vols., 8vo, cloth, $7.00. 

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investigator and every teacher who goes beyond the merest rudiments must needs 
equip himself. There is certainly no book in English — we think there is none in any 
other language — which covers quite the same ground. It records the most recent ad- 
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THE FUNDAMENTAL CONCEPTS OF MODERN PHILOSOPHIC 
THOUGHT, CRITICALLY AND HISTORICALLY CONSID- 
ERED. By Rudolph Euceen, Ph. D., Professor in Jena. With an 
Introduction by Noah Poktek, President of Yale College. One vol., 12mo, 
304 pages. Cloth. Price, $1.75. 

President Porter declares of this work that " there are few books within his 
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self with the course of modern speculation and scientific thinking, and to form 
an intelligent estimate of most of the current theories." 

MIND IN THE LOWER ANIMALS IN HEALTH AND DISEASE. 

By W. Latjder Lindsat, M. D., F. R. S. E., etc. 2 vols., 8vo. Cloth, $4.00. 

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comparative psychology, claims that he entered on his inquiry without any theory 
to defend, support, or illustrate. We are bound to say that, while his general 
conclusions are boldly and continually avowed, his claim of fairness and caution 
is justified by his method of examining particular phenomena ; that he seems 
willing at all times to renounce any impression or belief which is shown to be 
scientifically untenable."— New York Sun. 

"In this work— two volumes of over 500 pages— Dr. Lindsay marshals a pro- 
portionately large number of facts against those philosophers who maintain that 
the intelligence of man differs in kind aud not simply in degree from that of the 
lower animals. It is one purpose of his book to show that the main differences 
between man and the lower animals exist rather in their physical than in their 
mental structure. In this way of thinking, all animals possess not the semblance 
of, but the true substance of mind and will."— New York World. 

" So far as we are aware there has been no treatise upon the subject of animal 
intelligence so broad in its foundations, so well considered, or so scientific in its 
methods of inquiry, as that which has been prepared by Br. W. Lauder Lindsay 
in two large volumes, the first being devoted to a study of animal mind in health, 
and the second to animal mind in disease. We may safely say that his wcrk is, 
in some respects, the most important essay of the kind that has yet been under- 
taken. His observations have been supplemented by a thorough mastery of the 
history and literature of the subject, and hence his conclusions rest upon the 
broadest possible foundation of safe induction. There is a good analytical index 
to the book, as there ought to be to every work of the kind."— New York Evening 
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THE ELEMENTARY PRINCIPLES OF SCIENTIFIC AGRICULT- 
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A GLOSSARY OF BIOLOGICAL, ANATOMICAL, AND PHYSIO- 
LOGICAL TERMS. By Thomas Dunman. Small 8vo. Cloth. 161 
pages. Price, $1.00. 

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of terms for definition and in his clear exposition of their etymological and tech- 
nical meaning, as to leave nothing to be desired in this direction."— New York 
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A TREATISE ON CHEMISTRY. By H. E. Roscoe, F. R. S., and C. 

Schoreemmer, F. R. S., Professors of Chemistry in the Victoria University, 
Owens College, Manchester. Illustrated. 

Vols. I and II.— Inorganic Chemistry. Svo. 

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ing to be desired.'' 1 — London Academy. 

THE ELEMENTS OF ECON03IICS. By Henry Dunning Maceeod, 
M. A., of Trinity College, Cambridge, and the Inner Temple, barrister-at- 
law selected by the Royal Commissioners for the Digest of the Law to pre- 
pare the digest of the law of bills of exchange, bank notes, etc. Lecturer 
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Volume I now ready. 12mo, cloth. Price. $1.75. 
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ADOLPH STRECKER'S SnORT TEXT-BOOK OF ORGANIC 

CHEMISTRY. By Br. Joijanms Wi-licknus. Translated and edited, 
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science in its main facts and leading principles, as demanded by the systematic 
chemical student. We have here, probably, the best extant text-book of organic 
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prepared in a way to secure the greatest excellences in such a treatise."— The 
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THE ORIGIN OF CIVILIZATION AND THE PRIMITIVE CON- 
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By Sir John Lubbock. Bart . F. R. S., President of the British Association. 
With Illustrations. Fourth edition, with numerous Additions. 8vo, cloth. 
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SCIENCE AND CULTURE, AND OTHER. ESSAYS. By Professor 
T. H. Huxley. 12mo. Cloth, $1.50. 

" Of the essays that have heen collected by Professor Huxley in this volume, 
the first four deal with some aspect of education. Most of the remainder are 
expositions of the results of biological research, and, at the same time, illustra- 
tions of the history of scientific ideas. Some of these are among the most inter- 
esting of Professor Huxley's contributions to the literature of science."— London 
Academy. 

" When weary of the iteration of old thoughts dressed up in new phrases, it 
is refreshing to be brought into converse with one of the most vigorous and acute 
thinkers of our time, who has the power of putting his thoughts into language so 
clear and forcible. ,, — London Spectator. 

CAPITAL AND POPULATION : A Study of the Economic Effects 

of their Relations to Each Other. By Frederick B. Hawley. 

12mo, cloth. Price, $1.50. 

" It would be false modesty in me to seem unaware that the economic law I 

have attempted to establish equals in its influence upon economic conclusions 

any hitherto ascertained. Granted its truth, it throws new and decisive light 

on nearly all the unsolved problems of the science. 1 ' — Extract from Preface. 

PHYSICAL EDUCATION; or, The Health Laws of Nature. By 

Felix L. Oswald, M. D. 12mo. Cloth, $1.00. 

Contents : Diet, In-door Life, Out-door Life, Gymnastics, Clothing, Sleep, 
Recreation, Remedial Education, Hygienic Precautions, Popular Fallacies. 

" The author strikes right and left at the lingering traces of the traditional 
asceticism which has had so much influence in warpimr our systems of education 
and life. He insists, at the outset, that the monkish identification of the human 
body with Satan and sin shall be discarded utterly, and that we shall regard this 
tabernacle of clay as the most perfect structure of the divine architect, and as the 
sole means by which we can work out our salvation. Nature is the author's 
supreme law, and his cure for all maladies of the individual and the community 
is right living." — Home Journal. 

" Dr. Oswald is as epigrammatic as Emerson, as spicy as Montaigne, and as 
caustic as Heiue. "—Philadelphia Press. 

THE PRINCIPLES OF THE LAW: An Examination of the Law 
of Personal Rights, to discover the Principles of the Law, as 
ascertained from the Practical Rules of the Law, and har- 
monized with the Nature of Social Relations. By A. J. Willard. 
8vo, cloth. Price, $2.50. 
" A calm, dignified, able, and exhaustive treatise of a subject which is of great 
importance to every one. Mr. Willard first discusses the nature and origin of 
rights, obligations, and powers of fundamental social law and institutional law. 
He then expounds the science of law and defines the nature of all species of obli- 
gations and contracts. A aeneral view of rights and powers is then brought 
forward, and a consideration of their special functions, as, for instance, the use 
of air and water and the principles of individual sustenance. The doctrine of 
individual redress and protection is thoroughly examined, and a long and inter- 
esting discussion follows of nuisance", wrongs, and injuries. The characteriza- 
tion of dueling and the pithy and convincing way in which its absurdity is shown 
are admirable. The treatment of the subject is so clear and logical, so simple 
and scholarly, that it deserves the highest praise. It is a work such as Aristotle 
might have written, had he lived in this latter day."— Philadelphia Press. 

For sale by all booksellers ; or sent by mail, post-paid, on receipt of price. 

D. APPLETON & CO., Publishers, 

1, 3, & 5 Bond Street, New York, 



WORKS OF ARABELLA B. BUCKLEY. 



The Winners in Life's Race ; 

oe, THE GREAT BACKBONED FAMILY. With no- 
merous Illustrations. 12mo. Cloth, gilt, $1.50. 

Life and Her Children. 

Glimpses of Animal Life from the Amoeba to the Insects. 
With upward of One Hundred Illustrations. 12mo. Cloth, 
$1.50. 

Fairy-Land of Science. 

With numerous Illustrations. 12mo. Cloth, $1.50. 

" It deserves to take a permanent place in the literature of youth.'" — 
London Times. 

" So interesting that, having once opened the book, we do not know 
how to leave off reading/' — Saturday Review. 

A Short History of Natural Science and the 
Progress of Discovery, 
FROM THE TIME OF THE GREEKS TO THE PRES- 
ENT DAY. For Schools and Young Persons. With 
Illustrations. 12mo. Cloth, $2.00. 

"A most admirable little volume. It is a classified resume of the 
chief discoveries in physical science. To the young student it is a book 
to open up new worlds with every chapter." — Graphic. 

" The book will be a valuable aid in the study of the elements of nat- 
ural science." — Journal of Education. 



For sale by all booksellers ; or sent by mail, post-paid, on receipt of ijrice. 



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The Works of Professor E. L YOUMANS, M. D. 



Class-book of Chemistry. 

New edition. 12mo. Cloth, $1.50. 

The Hand-booh of Household Science. 

A Popular Account of Heat, Light, Air, Aliment, and Cleansing, 
in their Scientific Principles and Domestic Applications. 12mo. 
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The Culture demanded by Modem Life. 

A Series of Addresses and Arguments on the Claims of Scientific 
Education. Edited, with an Introduction on Mental Discipline in 
Education. 1 vol., 12tno. Cloth. $2.00. 

Correlation and Conservation of Forces. 

A Series of Expositions by Professor Grove, Professor Helmholtz, 
Dr. Mayer, Dr. Faraday, Professor Liebig, and Dr. Carpenter. 
Edited, with an Introduction and Brief Biographical Notices of 
the Chief Promoters of the New Views, by Edward L. Youmans, 
M.D. 1 vol., 12mo. Cloth, $2.00. 



The Popular Science Monthly. 

Conducted by E. L. and W. J. Youmans. 

Containing instructive and interesting articles and abstracts of articles, 
original, selected, and illustrated, from the pens of the leading scientific 
men of different countries ; 

Accounts of important scientific discoveries ; 

The application of science to the practical arts ; 

The latest views put forth concerning natural phenomena, by savants 
of the highest authority. 

Terms : Five dollars per annum ; or fifty cents per number. A Club 
of five will be sent to any address for $20.00 per annum. 

The volumes begin May and November of each year. Subscriptions 
may begin at any time. 

New York: D. APPLETON & CO., 1, 3, & 5 Bond Street. \ 



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